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SYSTÈMES LINÉAIRES
PIVOT DE GAUSS
DCG
CFA ACE PARIS
CHERMAK
DUT
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00:00:14
hello so today's theme
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is
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about linear systems we will therefore
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define what a linear system is
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learn to solve a linear system
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we will mainly base ourselves on the
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kid's pivot method and in
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a next sequence we will will therefore approach
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matrix calculation we will first start
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by quickly defining what a
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system is a binary system
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so first you need to know that your
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the word system means that we will be
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in the presence we will be in the presence of of
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several several so equation for
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example if I write if I write this that 2x
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plus y
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beijing 7 5x -6 y equals 13 this is a
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linear system of agreement
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linear systems including composed of two equations
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composed of two equations and of course
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here two variables so two unknowns
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so here you would have the coefficients 2
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to 7 are coefficients how d
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madonna after a more
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generous writing so that too is a
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binary system x plus y plus z equal to 8 3 x +
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5 y or plus
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six legal aids cat
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so that is also a linear system
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so this time of two equations with
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three unknowns
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then we can have
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we can have quite the writing
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like this so often we pride it this
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type of writing by example not see 2 x
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ore +62 equals 8 - 5 x 1 - 5 x 1 + x 2
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- x3 equals 7 and finally x1 +8 x3 equals
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say so here you also have a
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linear system so three equations
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this time with three unknown x1 x2
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x3 on the other hand which is not a
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linear system
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it is a system which would appear
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as follows 2 x squared plus y equals 8x
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squared - 5 y squared and cassettes for
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example this this is not a
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linear system so generally in a
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binary system
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you of course always always have a
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form of the type ax to x b y these aids et
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cetera et cetera mega command and you
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always have a power x the
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power a y to the power to etc
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so if I take if I just take if
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I just take a linear equation of
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this type 2 x - y
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- 3 and gain 0 so here we have a
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linear equation and of course the set
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of solutions of this linear equation
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that we can write in a reduced way
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as well as the set of solutions of
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this linear equation it is quite
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simply cross the set is this it is
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the set of couples xy
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is it not it is set of cuts
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xy such that y is equal to 2 x -3 and of
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course with
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European xy
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we will say rather a reference yes j so
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if I represent the set of
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solution of this equation
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it is quite simply the points the
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points belonging to the straight line
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of Cartesian equations 2x minus y -3
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equals zero so that this right there it
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will go through the points
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the solution 6x equals 0 and 6 x equals zero y
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were much less 3 so that's a
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solution
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another solution if x equals the x equals
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two schools y is equal to how many votes
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of 4 4 - 3 1
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therefore y equals or which simply gives me
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0 - 3 c this first point 2 1
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2 1
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it is this second point therefore all
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the solutions of this equation are
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represented therefore not the line which here
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then so in this in this
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sequence I will rather I will try
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to I will actually try to
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find
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a situation which can interest the
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greatest number so in
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general this this sequence there it will
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not be too too too too
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mathematical
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so it will rather be will rather be of
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great use to people who
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need a little operational research
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and in particular all people
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registered in dcg in the context of
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management control where we necessarily have to
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manipulate systems from time to time,
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particularly when we we are dealing with
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crossed services when we have two
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auxiliary centers it's still okay but
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as soon as we start to have 3 4
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auxiliary centers things start to get
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complicated so as soon as we have to resolve
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a system in which a system where
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indeed we are faced with
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several several unknowns three
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four five unknowns
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we of course need a method resolution methods
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this is what we will try to see in 7
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56
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so we will therefore give a
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somewhat general writing of a binary system
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so we are going to give ourselves two integers or
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two natural integers small hatreds and
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small p isn't it so it is two
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natural integers small hatreds and little
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cheap and therefore a linear system a
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binary system 2n hatred equation
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ap equation unknown therefore a system binary of
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hatred equation
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ap unknown okay ap unknown is a
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system of the type I write it it
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will appear like this then doc to 1 1 x
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1 to 1.2 to 1 2 x 2
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I continue like this we said we said n
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is what you pay unknown so little
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unknown we will therefore have here x a
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panel at 1 p at a pxp equal to b1
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this is my first equation okay
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this is my first equation second
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equation so here I am in first
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line 2nd goal at 2 1x at 2 2 which ensures
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plus more plus
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then at 2 2 x 2 plus a2p xp and curved 2
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and I continue like this we said
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an equation so we will therefore have n line
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therefore the first the first index
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which is the line number so second
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line nth line and the second index
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here is the column number so
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here first column so to it one x1
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plus to l 2 x 2 plus to haisnes pxp equals
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bp so this is a linear system of
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hate
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equation l equation
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ap unknown the unknowns are x 1.6 2 x
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p the hadjis the ifi i.e. aaa to
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1.2 to 2.2 to an ip agreement the in fiji
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are real coefficients bab2 bp are
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coefficients real so you are here
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in the presence of a linear system which
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is composed of hatred
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hatred equation
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ap equation unknown okay linear systems
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of hatred ap equation suddenly you so
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now we're going to move on we're going to move on to
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the resolution to the resolution of system
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we will start with very
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simple things so that everyone understands
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because the idea
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the idea is not to leave
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anyone behind
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whatever your level you can
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always somewhere between is in the
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sequence either moving forward or
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backward it's up to you so if
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I have a system like this I
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write it like this for example Thursday
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2x plus y equals quickly and there I say y
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also so there I have a
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linear system of two equation with two
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unknowns
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the solution evault natively sand
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since I have y equal 2 I only have to
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replace y/y equal by its value in
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my first equality so what do
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I obtain I obtain noc 2x more
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damage 8 with y equal to which gives me
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a system equivalent to 2 x equals 6 y
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equals 2 and finally to finish x equals 3-6 /
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2 and y is calm therefore the solution of this
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system there a solution of this system there
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is the couple 3 of romandie x equals 3
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and y equals 2 then we can take a
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system a little more a little more I
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would say a little more elaborate so if we
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take a system like these for
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example I say 2x plus y 8
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x y and dinsheim for example solution of
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this system there then of course we will
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actually use it but when we have
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a system of two equations with two
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unknowns
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there are several resolution methods
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so I will start with the
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most elegant method we will say the
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substitution method so which consists of doing
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what to express one of the variables as a
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function of the other so here we can
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simply have x y is equal to 5 -
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x okay I'm going to replace
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above so that makes 2 x plus and I
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replace y by its value above
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which gives you is indeed 8 and so there
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you have a system this system is
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equivalent to the previous system okay
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and so there you noticed that I
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got rid of 'one of the unknowns y by
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replacing y with savan I expressed here
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I expressed y here as a function of x so
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I replace and pass y in value here
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so now we do the calculation which
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I will let you do quickly
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you have it 2x minus x that's
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simply
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I found the problem that it is only at 3 but as
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y is equal to 5 - x so there are guards
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simply 1 5 - 3 which makes x
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equals y is equal to two and we can
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also check three that makes 5 2 x 3 6 6 + 2 that
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makes 8 so the solution the solution of
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this system
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is quite simply the couple 3 2
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okay the solution of the system is the
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couple 3 ok
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so the substitution method and is
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all quite indicated when you have a
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system of two equations two unknowns
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possibly three equations three
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unknowns but already at 3 equation with three
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unknowns
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this method turns out to be very very cumbersome
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since you have very neutral you will
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actually manipulate
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hot clothes and it is so it's really a
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source of errors that's why
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I insist we will very quickly
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adopt a resolution method
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whatever the type of equations
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resolution methods which barely fits
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the pivot method
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kid pivot then the idea the idea the idea is
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this then the idea is this
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the idea is this when you have
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in what you have a system I
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would take system of how would I say
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of 3 equation with three unknowns
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you understood that if I have a system
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like this and there I write x y or z
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also 12
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there I will shout y more than z we
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also have gains of 6 and there I will
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write z and gain them to 4 you have
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understood that the solution of this system
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is relatively easy the only thing if
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it is relatively easy quite
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simply because here we have
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the downstream in two and five years help equals 4
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so it suffices to replace z by four
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here to deduce the value of y
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once I have found y knowing z
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knowing y
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I just have to replace y and z by
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their values ​​to deduce the value of
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x1 so this system we say that this
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system a triangular shape
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that is to say that this system there it
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presents itself thus dan well it
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presents itself thus it presents itself thus
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why because there you have there you
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have y is x learn y and z
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and there you have x y and z
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d 'okay which means that below
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here we don't have an x ​​it's as if
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here I had 1 0 and of course we do
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n't have an x ​​here it's as if here I had
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1 0 and there below y
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I don't have any x so this system I
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can write it like these 0x okay
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and here I can write it 0 x + 0 y plus
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zen it's exactly the same type of
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that more simply another writing
00:17:15
of what I had written previously
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so this system there it presents therefore it is
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simply called a
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triangular comand system and we can say that
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even written like that it is a system
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it is a staggered system
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then that is to say that in reality it is
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staggered why because when you
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have gone from one line to the next line
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you always have one more zero see
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the next line always starts
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always starts with 1-0 additional
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the club starts with a ski at a fixed the
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next line I start with a zero
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and the next line I start again
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with an additional zero okay I
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start with an additional zero what we will
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therefore call a staggered comand system
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so here so if indeed if I
00:18:13
have to solve it so I'm going to manage
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that it a little bit what we have here
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we're going to so that so the resolution
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of this system again is
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relatively easy so here we have l
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equal to 4 and I go back since z equals
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4 2 x 4.8 so y is simply
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equal to 6 - 8
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that is to say 1 - 2 and I only have to go
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back the value of y is 4 and
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my two aids
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here that makes me minus 2 + 4 that makes
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2 - 2 + 4 that makes 2 that of course I
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add one on each side
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that makes 12 - two that makes exposing in front
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equalizes so the solution of this system
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this time here it is no longer a couple
00:18:59
but what we call triplet so it is
00:19:02
a triplet 10 less than four installer
00:19:09
in general we had a system of
00:19:12
hatred equation of an equation
00:19:14
ap unknown grant just now we
00:19:17
therefore had the general writing of a
00:19:19
linear system of 1 equation ap
00:19:23
unknown in this case the solutions if
00:19:25
it exists agree it is not always
00:19:27
the case and it is a society exists it
00:19:30
will therefore be n will say nodes peeled
00:19:33
agree aids of the hockey plan
00:19:45
ok
00:19:47
rather since so there it is triplets
00:19:50
how she had defined during
00:19:53
grandpa unknown so cop forgotten ok then
00:19:58
this 7th this writing there this
00:20:02
writing there so our system is
00:20:06
presented like this then them now
00:20:11
now when we have a system at the
00:20:14
start we will have to therefore the idea the idea
00:20:19
is from a system data
00:20:23
from a given system agree
00:20:27
to be able to build to finish with
00:20:32
first a system of cho les and after
00:20:35
what I would call a
00:20:37
reduced staggered system the freelance would explain
00:20:41
through an example so the idea
00:20:43
the idea is from a
00:20:44
proposed system trying to end up with
00:20:48
something a format that looks like this one in
00:20:50
other words try to finish with what we
00:20:53
call a system that we call
00:20:57
triangular okay a triangular system
00:21:02
ok so we're going to take a
00:21:06
numerical example and we're going to explain then what we
00:21:10
need to know first. is that you
00:21:14
will have to manipulate linear systems
00:21:17
in other words you will go from a
00:21:19
linear system to an equivalent linear system
00:21:22
so the method that we will
00:21:25
put in place
00:21:26
of course will not call on this
00:21:32
notion of operation of operations
00:21:35
on the lines when I say operations
00:21:38
on the lines of operations on the
00:21:41
equations proposed I use the word line
00:21:43
because each equation we will give it
00:21:46
the letter it for example
00:21:48
equation 1 it will correspond to
00:21:50
the alignment the equation it
00:21:53
will correspond to the line it says
00:21:59
when we see what we will apply
00:22:03
as a rule to pass from a system to an
00:22:07
equivalent system we will allow ourselves the
00:22:12
following operations I fart to pass
00:22:14
from a system to an equivalent system we will
00:22:18
allow ourselves the following operations
00:22:20
we will first be able to
00:22:25
rather not be authorized to make
00:22:30
line changes in other words if
00:22:31
I have an equation in the first line I have
00:22:34
a third equation real prohibits me
00:22:36
from 'inverting to put the third
00:22:38
equation in the first line and the
00:22:40
first equation in the third line
00:22:42
is what I call inverting the order
00:22:44
of the cities and therefore the codification is
00:22:47
this one the codification of this one I
00:22:49
will therefore when I 'write that she reads
00:22:51
double arrow she j that means I
00:22:57
coty girl my operation indicating
00:23:01
that I have allow line 1 line
00:23:04
10 by whose equation of rank and and
00:23:07
the equation of rank j our first
00:23:10
operation other operation another
00:23:13
operation
00:23:14
we can replace an e lee an equation
00:23:19
the coding this one starts with a
00:23:25
deer a scene a certain number is
00:23:27
multiplied by this equation I will
00:23:29
say by able alpha it says plus plus
00:23:35
the equation obtained on line j that's it
00:23:41
an operation that we are going to allow ourselves
00:23:44
let's take a very simple example if I
00:23:47
take a system like this yes I
00:23:50
take a very simple system like this
00:23:53
+2 y equal 8
00:23:58
and there I say there I say for example x
00:24:02
plus
00:24:05
y equal or 5
00:24:12
I am going to apply one of its rules here
00:24:15
here I am going to write here I am going to write
00:24:18
here I am going to write she inverted
00:24:25
with her first two steps I
00:24:29
indicate I indicate here the inversion of
00:24:33
the equation up and the locations of that I
00:24:36
translate so the system that I obtain
00:24:37
is necessarily a system equivalent
00:24:41
to the previous system
00:24:42
so what am I going to have here I
00:24:44
am going to have this I am going before x plus y
00:24:48
equals bag and of course here I am going to have
00:24:52
3 x + 2 is parked there so there I carried out
00:24:57
this operation
00:24:58
now as I told you
00:25:00
previously the idea the idea is to
00:25:03
determine a triangular system
00:25:06
in other words the idea these two of having a
00:25:09
zero here is to have a zero here and there
00:25:12
I will therefore carry out an operation on
00:25:15
us in equation 2 of ocz which I played
00:25:17
titled like this and I will write to
00:25:21
have a zero here it is necessary that at 3 x I
00:25:24
add to it - 3 x org the g + 1
00:25:46
at o2
00:25:48
later we will take three unknowns
00:25:50
we will also learn four unknowns what is
00:25:54
needed what is needed
00:25:55
why this writing is
00:25:57
interesting because it allows you
00:25:59
it allows you at any time to
00:26:01
check your calculations in other words you
00:26:04
can stop the process was going to
00:26:05
have a coffee and come back and start again
00:26:08
whereas if you network
00:26:10
like this steve by other methods you
00:26:13
risk actually you have to
00:26:14
start and you have to finish it and if
00:26:17
you ever have difficulties you
00:26:19
meet divinity it is very very
00:26:21
difficult to detect the ranks while
00:26:24
there everything is recorded all the
00:26:26
calculation steps sow instructions and since you
00:26:29
can check them systematically
00:26:32
so here this system there is
00:26:36
equivalent this system so these two
00:26:38
systems are and who will now this
00:26:41
system there is equivalent to which system
00:26:44
look carefully can I write
00:26:46
yes so x plus y equals 5
00:26:50
and now that I am going to apply my
00:26:52
rule -3 l1 so me 3x plus 3 x that makes
00:26:58
zero x yes the vix index pap
00:27:01
so see there I I started my line with
00:27:03
a year there I'm going to start my line with
00:27:06
1 0 this is what we call a
00:27:07
two-day staggered system one more zero
00:27:09
compared to the previous year
00:27:11
okay and so is here I give
00:27:17
me 3 l job and -6 plus l2 - 6 + 1 - 5
00:27:26
- 5 there's guy minus five there's gain is
00:27:32
so I make minus 3 l
00:27:34
a month 24 - 24 +5 -24 +5
00:27:43
that's minus 19 d' agreement or 1.24 chipk
00:27:49
that makes negative nineteen and you
00:27:50
obviously understand the solution it is immediate
00:27:54
so you have here y equals 19 5th and of
00:28:00
course x quite simply equal to 5 - y
00:28:05
therefore 5 - 19
00:28:07
fifth which makes 25 5th - 19 5th
00:28:12
which is simply 6.5
00:28:15
we can check if fifth plus 19.5
00:28:18
to you have 25 5th and how would I say
00:28:22
three times 6 10 8
00:28:25
two times 9 38 18 + 18 + 38
00:28:33
it looks like three times of 6.18 two
00:28:38
times 19 38 so 18 + 38
00:28:44
so there is a small error perhaps
00:28:46
somewhere
00:28:49
so we actually have a house of
00:28:52
2 well note the writings which
00:28:56
are there so you have you have
00:28:58
obviously seen that I I had made a
00:29:00
mistake so here when I applied my
00:29:03
rule here so the equation two suffered
00:29:06
-3 l man plus l2 therefore minus three l1 -
00:29:11
3 x can 3x ap the goods zero but
00:29:13
minus 3 she knows minus three y + 2 y
00:29:18
I repeat - 3 l1 it's negative three y +2
00:29:22
y so there I made a little mistake
00:29:24
it's here - y
00:29:25
isn't it so here I'm going to erase
00:29:27
because so that's wrong so here I
00:29:30
am going to correct so here we said y
00:29:32
okay - then there is -3 l1 - 15 + 8
00:29:39
- 15 + 8 that makes minus seven I ca
00:29:43
n't at all for myself I try to
00:29:44
find minus 19
00:29:45
but still one times it has the merit it
00:29:49
deserves it so explain exactly the
00:29:52
herbs - troyes - 15 + 8 which gives me a
00:29:55
system equivalent to legal y this agreement
00:30:00
y therefore equals 7
00:30:02
and then x is quite simply equal to 5
00:30:06
- that salaries x equal to minus 2 so
00:30:09
the solution of this system
00:30:10
is much less 200 ok and of course we
00:30:16
replace or 16.6 since one when that
00:30:19
makes 8 and of course - 2 + 7
00:30:23
that makes five so there you see that
00:30:28
the manipulations which are there are
00:30:31
relatively relatively heavy
00:30:33
so I'm going because their advance and I do
00:30:37
n't want either again each
00:30:38
time I say it I'm overflowing but this
00:30:40
time I'm going to stick to it
00:30:43
so a relatively short video but
00:30:45
once again quite precise
00:30:49
So this time I'm going to take a system of
00:30:52
three equations with three unknowns and we're
00:30:56
going to try to explain and give
00:30:59
a solution method
00:31:03
so there I have a system so that
00:31:06
you see here I insisted 1-2 -3
00:31:08
equation with three unknowns so that I
00:31:11
give you 2x minus y since one was
00:31:13
dice 9 and we have here three y
00:31:15
drew damage lemoine 2 and x + 2 y +3
00:31:20
help equals 9
00:31:21
of course I can adopt the
00:31:25
previous codification and so solve to the system
00:31:29
to determine to find what we
00:31:31
call a triangular system or quite
00:31:32
simply a staggered system agree
00:31:36
to do this to do this so we will
00:31:40
therefore have to use the method therefore the
00:31:42
kid's pivot method that I am going to
00:31:43
try to detail in front of you and
00:31:47
then you so I give you
00:31:49
another method which allows us to find
00:31:50
what we call directly the values
00:31:53
of x and y
00:31:54
with your word on what we call a
00:31:57
unit matrix that I will do it I
00:31:59
will do at the end although this aspect I
00:32:02
addressed in a previous video that
00:32:04
I titled therefore resolution of a
00:32:07
system by the kid's pivot method
00:32:09
so here what I suggest you
00:32:11
do because I don't want to either
00:32:13
solve it here then after give you
00:32:15
our writing method what I
00:32:17
ask you to do is to transform this
00:32:20
system into an equivalent system but
00:32:24
instead of presenting it like this we are going to
00:32:26
adopt as we are going to adopt a
00:32:30
matrix writing finding says we are
00:32:33
simply going to transform this system
00:32:36
into a matrix which will be one on the d20
00:32:42
so here I write I take the coefficient
00:32:45
2 royer minus 1.4 I will transmit there
00:32:52
I write my second member
00:32:53
9 then the issue is not no x so there
00:32:57
I have zero the g3 the ga and there I have less
00:33:04
so I take a last equation of
00:33:08
ax +2 y +3 also help here so this
00:33:16
system is presented in
00:33:19
table form it is easier to manipulate
00:33:22
these quantities than to have to each
00:33:25
time rewrite x y and z launched more
00:33:28
it is simply for convenience first
00:33:33
thing first thing first rule
00:33:34
since it is a kid's pivot method
00:33:37
when you have a choice when you
00:33:39
can have a pivot equal to 1
00:33:41
we must of course favor this
00:33:44
possibility so there you see that my
00:33:47
pivot here since I want to find
00:33:49
I want to end up with a system which
00:33:51
looks like this so here I would like to
00:33:59
arrive at that I have three unknowns I
00:34:01
would like to arrive at a system which
00:34:03
looks like that so that's a
00:34:11
step system and of course I have nothing but
00:34:12
here because the cd 0 2 0 2 0
00:34:14
ok so there it is indeed a
00:34:17
triangular system a step system then
00:34:22
in the coding so there you see
00:34:24
very well that in the last line gsi
00:34:28
at 1 so it is an interesting pivot
00:34:31
what am I going to do
00:34:32
first rule I am going to invert so of
00:34:35
course never never you will have a
00:34:38
pivot equal to zero between man 10 le le
00:34:41
fact that the zero is there if you
00:34:43
invert and 7th line
00:34:45
this equation to this equation there you
00:34:47
will end up with a zero here and
00:34:49
0 cannot be a pivot okay
00:34:52
ok so but what I can take two
00:34:54
as a pivot is closed calculation okay
00:34:57
I can do that but it is to give you
00:35:00
the simplest method to precisely
00:35:02
achieve the goal as simply
00:35:05
as quickly as possible so here what am
00:35:08
I going to do I am going to change what
00:35:10
is there and so I'm going to say
00:35:12
swap and line a and
00:35:15
line 3 says swap line to
00:35:20
line 3 so I'm going to get a
00:35:22
I write simon new table so I'm going to
00:35:25
get x 1 2 3 9 passes I'm
00:35:33
wrong
00:35:34
then this line is unchanged and
00:35:41
of course I swapped line a and
00:35:43
line 3 so here I have 2 - 1 4 lfg
00:35:53
twice 9 do I have two times 9
00:35:54
the answer is no it would rather be here
00:35:57
1 3 so there I have 23 and therefore the g13 is
00:36:07
therefore there obviously I would have 1 3 ok so
00:36:13
here I am just looking if my system and the
00:36:16
beautiful very good rule number 1
00:36:20
it is therefore necessary firstly firstly
00:36:23
determined to choose the well will therefore the
00:36:25
pivot here the pivot here this will be my well
00:36:30
also go to the quay and so I will
00:36:33
arrange to have zeros
00:36:36
below the pivot okay so there it is
00:36:38
already done
00:36:39
this line there will remain unchanged since
00:36:41
the maps at 1 0 I will c is therefore
00:36:43
to have a zero here so to eliminate what
00:36:46
to eliminate the famous the famous x here I
00:36:49
am going to apply the following operation
00:36:51
I am therefore going to change line 3 and in
00:36:55
line 3 what am I going to do do
00:36:56
I'm going to do minus twice l employee
00:37:00
- 2 + 2 - 2 + 2 so I write less of l
00:37:04
a plus now
00:37:09
it's worth showing you to
00:37:13
show you the calculation is so I'm
00:37:15
now going to find a table equivalent
00:37:18
to the previous table
00:37:19
there my first line is unchanged 1 2 3
00:37:25
9 031 -2 I do my operation
00:37:33
- 2 it has less than more than 0 - 2 it has
00:37:40
- 4 - 1 - 4 - - 5 - 2 it has more l 3 -
00:37:49
6 - 6 + 4 - 2 - 6 + cap - 18 - two
00:38:01
Germans -18 + 3 - kate - 18 + 3 - 18 +
00:38:14
3 points 4
00:38:22
so here we have a system so
00:38:24
here of 3 equation with three unknowns therefore
00:38:27
2x minus y since it is legal 9.3 y
00:38:31
plus it releases less than 2x more than y
00:38:33
+3 aid equals three years of course I can
00:38:38
apply the previous codification to
00:38:40
this system to find an
00:38:41
equivalent system isn't it but I
00:38:44
of course suggest you present the
00:38:47
calculations otherwise instead of manipulating
00:38:50
this writing we are going to transform this
00:38:53
system using a table
00:38:55
in other words we are going to use
00:38:57
matrix writing so this system we can
00:39:00
translate it
00:39:01
we can translate it by the table
00:39:03
following the rule we can translate it by
00:39:06
the following table shows the
00:39:07
coefficients 2 - 1 4 there I was ultra
00:39:16
waisted I put my world right 9
00:39:18
then there is no x so 0.3 to and
00:39:26
-2 then here 1 2 3 and round in other
00:39:38
words this writing there I will
00:39:41
prefer the system written in the form
00:39:45
of a table so the idea the idea is
00:39:50
to say this
00:39:51
the idc degree of this system which we said
00:39:53
by the kid's pivot method
00:39:56
from a system presented thus we
00:39:59
must arrange to have what we
00:40:00
call a triangular system
00:40:03
triangular therefore superior indistinct
00:40:06
triangular therefore which presents itself thus
00:40:08
here we have the three unknowns here
00:40:11
we have our two unknowns and if we
00:40:14
have a only unknown
00:40:16
of course there you have the
00:40:19
right member so here the system is well
00:40:21
scaled since the g10 the
00:40:24
ayrault ag and there I have zero on each line
00:40:27
we have a baby on 1.0
00:40:29
additional so the idea is is to
00:40:31
say how I go from this table to
00:40:34
a table that looks like this
00:40:38
so first thing we are going to
00:40:42
apply our rules so the idea is the
00:40:44
first thing you need to know
00:40:46
you can never have a pivot
00:40:50
equal to zero the bed here is to
00:40:53
choose your pivot
00:40:54
so we will start with the first
00:40:56
line but when we have the choice of having
00:41:00
a pivot equal to 1
00:41:01
we must of course favor it privately
00:41:04
is therefore this choice to notice that
00:41:06
here I have unis and there I have another line
00:41:10
there I have a coefficient equal to 1 so what
00:41:12
I am going to do I am going to invert
00:41:15
line a and line 3 which I am going to
00:41:18
code like this so here I am writing line ea
00:41:22
line to reverse swap with the line
00:41:27
too which will give me a table
00:41:30
equivalent to raising the shots here so at
00:41:35
2.3 and the world on the right is too
00:41:39
I write my second line which is
00:41:41
unchanged 0 3 1 - 2 and finally as I
00:41:48
inverted first equation is 3rd
00:41:51
equation I copy my third here which
00:41:54
takes the place of the which goes in place
00:41:57
of a third so were in first
00:41:58
position
00:41:59
so here is a table a system
00:42:03
equivalent to the previous system
00:42:05
now the idea c is to remove
00:42:08
having a zero here okay on the
00:42:10
column below the weight double pivot
00:42:12
here we are going to choose one as pivot and so
00:42:16
we are going to transform this line line 3
00:42:19
equation 3 we are going to do to it what we
00:42:22
want have a zero here
00:42:25
so there I'm going to do minus twice to
00:42:27
+2 so I'm doing less than l1 + 1 3
00:42:34
you understood that if I do less
00:42:36
than l1 plus these three it will make me less
00:42:39
than more than 5 0 so we're going to do our
00:42:41
calculations then we do our calculations so
00:42:44
here my there the first equation is
00:42:48
unchanged so the world on the right also
00:42:52
my second line is unchanged and my
00:42:58
third line in fact less than l1
00:43:01
plus them 3 - 2 + 2 0 - 4 - 1 - 4 - 1
00:43:10
of which ranked 0 - 4 - to - 5 - 6 + 4 that's
00:43:18
minus two and be careful -
00:43:22
6 + 9
00:43:24
that's plus 3 very good so here
00:43:29
once again is a system equivalent to the
00:43:33
presidential system and keep and
00:43:35
writing I would have had what here and x + 2
00:43:38
y +3 and shift 3.3 y plus it is equal to
00:43:43
-2 and of course minus five y -2 helps
00:43:47
equal
00:43:48
once again it is much more
00:43:50
practical to do so presenting it like this
00:43:52
saves us from dragging around
00:44:07
I place myself here so the pivot
00:44:10
could be this one so we
00:44:14
have to arrange to have a zero here
00:44:17
so we are going to modify line 3 and therefore
00:44:20
line 3 what do I do to
00:44:22
have 1,066 it would be necessary that I have 3 / 3
00:44:26
to make 1
00:44:27
it is therefore necessary in reality that
00:44:29
I must have that I multiply the line e laly
00:44:31
place two by five to the third of l2 and
00:44:40
if I make 5 yesterday of l
00:44:42
2 3 / 3 that does 1 and 5 times that makes 5
00:44:48
but like much less 5 + 5 - 5 safra 0
00:44:52
so I do once again
00:44:54
saint-pierre of l2 +13 so saint-pierre
00:44:59
of s2 plus these three then do
00:45:02
I have the place to make a table
00:45:04
here I'm going to try I think so that's
00:45:07
okay the 7th line
00:45:10
the first line is unchanged here the
00:45:16
second line is unchanged and my
00:45:21
third line of course here I can
00:45:25
do the calculation
00:45:26
if I do saint-pierre of l2 saw 5
00:45:29
it will always be 05 yesterday 2-0 the more she
00:45:32
is more 0 her sentence dunlop the bench five
00:45:35
rings 00 +0 that's zero here there's no
00:45:39
problem we will
00:45:40
automatically have our two heroes who
00:45:42
appear now the weather is nice
00:45:44
calculate it is of course I check 5/3 x
00:45:47
3 that makes 5 5 - 5
00:45:50
that makes 0 then here I do 5
00:45:54
yesterday be careful not to use your verb 1/5
00:45:57
less than 5 yesterday - 2 that therefore makes 5 yesterday
00:46:03
- 6 /3 5/3 - 6/3
00:46:07
that's a third for me I repeat
00:46:11
fifth time one less than 5 yesterday - of
00:46:16
these five stones - 6/3
00:46:19
attention fifth times minus two that
00:46:22
's less than a third less a third plus
00:46:25
3 - 10 yesterday +3 it's less than a third +9
00:46:31
thirds so less said yesterday so sorry
00:46:33
it's less two so I'm repeating myself said
00:46:38
yesterday +3 so less than a third +9 thirds that
00:46:41
gives me
00:46:42
a third is so there I have well obtained a
00:46:47
superior triangular system therefore a
00:46:50
staggered system okay and there you
00:46:53
see I can now have fun
00:46:56
rewriting my system
00:46:57
I will still continue very
00:46:59
simply what I am going to do here what
00:47:02
I am going to do here I am going to write
00:47:04
for really wrote the thing I'm going
00:47:07
to write in line 3 I'm going to multiply
00:47:10
lille 3 by -3 I'm going to do negative three
00:47:15
l3 and I'm going to take my calculation again is a
00:47:19
little bit higher I'm going to take your
00:47:22
earnings a little bit higher and
00:47:25
I'm going to take it again here so the first
00:47:27
line is unchanged 2 3 and 3 the second
00:47:36
line is unchanged 031 minus the
00:47:43
third line and x - 3 which gives 0
00:47:48
01 and is now I can have fun
00:47:54
rewritten and my system
00:47:57
starting from the bottom jay z and gala
00:48:02
I write my second equation 3 y plus z
00:48:07
that I found here for more help is
00:48:11
equal to -2 and finally my first equation
00:48:14
x + 2 y +3 help equal to 3 I have
00:48:23
no scaled system and I am therefore going to
00:48:26
copy is calculated so that is
00:48:29
equivalent to z equal 1 so if it is legal
00:48:35
ah I pass the 1 in the other member
00:48:38
too told me I add minus one on
00:48:40
each side of which it will be minus 3.3 y
00:48:43
equals minus 3 that means that y equals
00:48:47
minus-13 there be the minus three years I
00:48:50
replace it's been so
00:48:52
n2 +3 I repeat there's minus that's
00:48:56
minus 2/3 1/3 - 2 + 3 it's been a year since
00:49:03
I pass that I add - hour on
00:49:05
each side too before one that gives me x
00:49:08
equals 2 so the solution the solution of
00:49:12
my system is the triplet of is
00:49:15
n't it - 1
00:49:20
it's the triplet 2 - 1
00:49:27
then I wanted to make I wanted to make
00:49:32
a remark yes so there I spoke of
00:49:34
two systems of staggered systems
00:49:37
but I could have had a
00:49:40
reduced staggered system that is to say that in
00:49:43
reality in reality but I think that at this point
00:49:46
it is already quite a lot
00:49:48
now what we could have done what we
00:49:51
could have done is that here we
00:49:54
could have arranged
00:49:55
we could have arranged to present
00:49:57
things like this
00:49:58
so let's admit let's admit that that I
00:50:02
want a system staggered how would
00:50:07
I say reduced so I have this
00:50:12
[Music]
00:50:13
I erase that well I'm going to erase all that
00:50:15
since the system now you
00:50:17
understand we have solved what I
00:50:20
can do here is to say hey I'm going
00:50:22
arrange to have a pivot and gala
00:50:24
offer so here I'm going to change line
00:50:26
2 and I'm going to do so a third of l1
00:50:30
takes l2 and so I'm going to get a
00:50:34
system equivalent to this system in a
00:50:36
table the following table will be 2 3 and 6
00:50:40
3 so there 011 third yes that's why
00:50:47
minus 2/3 0 - 5 - 2 3 so there your
00:50:58
pivot is equal to a trauma said the idea
00:51:01
is to end with that
00:51:02
the units matrix to have the 1 the 1 the to
00:51:05
agree finally matrix matrix I'm not going
00:51:10
diagonally like a triplet on 6.1
00:51:13
triangular with with argonauts
00:51:17
main so here now you
00:51:19
can do your calculation l3 but see
00:51:22
afterwards it's true that I don't I no longer have the g
00:51:25
the economy of the fraction but I'm
00:51:27
still going to 1/3 the minus 2/3 that
00:51:30
I have to manage so here I can do l 3
00:51:33
it's to have so that it makes 0 here
00:51:35
I have to make plus 5 - 5
00:51:38
so I do 5 l2 again 5 + 1 3 so here
00:51:44
I can do the calculation a little
00:51:46
bit higher so I do the calculation a
00:51:48
little bit higher which would
00:51:50
finally give me I hope I don't get
00:51:51
deceive because there can quickly so there
00:51:54
it makes 1 2 3 p 3 so there we said that
00:51:59
it's 0-1 a third isn't it the
00:52:03
minus two thirds
00:52:04
so there we said that we make 5 l2 then
00:52:06
the 3 of which Claude goes it makes zero
00:52:08
so the safra 015 l2 it makes 5 stone
00:52:12
months it 300 yesterday - 6/3 6/3 6/3
00:52:17
that makes less a third isn't it
00:52:20
then we make 5 l2 - said yesterday + 9 thirds
00:52:25
and that's negative a third and we end up
00:52:28
with what we say at the time since I
00:52:30
want a reduced staggered system
00:52:33
so I'm going to transform it into a straight line by
00:52:34
making negative three l3 and if I do
00:52:39
negative three l3 j 'get so I'm going to
00:52:43
erase here watch out there I'm holding so
00:52:46
this time I'll have this time a
00:52:49
reduced scaled system so go see what
00:52:52
I'm going to have a bit of e3 a here
00:52:58
so zero one third minus two thirds
00:53:04
0 0 1 and 1 is so of course now all that
00:53:12
remains is to translate my
00:53:13
system I of course have z equal to and I of course have
00:53:18
y plus a third of z also and two
00:53:24
thirds and I finally have x + 2 y + 3 help
00:53:31
equals 3 is so there you see very clearly
00:53:34
that you have a
00:53:36
triangular system being and there you have
00:53:39
breasts diagonally main since
00:53:41
I have that's why we talk about
00:53:44
reduced staggered system when the
00:53:47
coefficients here on all equal so I
00:53:52
now propose to take a system
00:53:54
of four equations with four unknowns
00:53:56
and then there you go then once again
00:54:01
it's 10 to one so I
00:54:04
don't know
00:54:05
ok I'm going to erase all that
00:54:10
very well others this time we are going to
00:54:11
take a system of four
00:54:13
equations with four unknowns
00:54:14
I had it and previously so I
00:54:16
made a small error that I had to
00:54:17
correct that you say do the calculation
00:54:19
quietly in the order that here we
00:54:21
also have century is presented like this
00:54:22
so x -3 y plus z - is also a
00:54:26
3 1 it's well minus three yes then
00:54:29
3x plus they draw from it 2 n equal to both
00:54:32
y - 5z track also 1.7 and finally 2x
00:54:37
minus y +3 is more and more you
00:54:40
are not equal 13
00:54:42
so we have to determine a
00:54:44
quadruplet if it exists since this system
00:54:47
cannot not have a solution it
00:54:49
turns out that it was once again that
00:54:50
once again j I did an evaluation so
00:54:53
the quadruplet x y z must be determined
00:54:56
then the idea first so transform this
00:54:59
system into the form of a
00:55:02
matrix table following the ag which therefore
00:55:05
makes at least 3 2 - 1 is less
00:55:15
then 3 1 2 is in neither two there
00:55:22
is no tea our zeros and then 11
00:55:25
there is no x so 02 - 5 1 - 7
00:55:36
finally the fourth equation 2 - 1 3 1 and
00:55:48
stay good there I kept myself to have
00:55:52
inverted the lines I started by
00:55:54
directly having a pivot here just to
00:55:58
go a little quickly although the calculation
00:56:00
will still be relatively long
00:56:01
so step number one
00:56:04
we will therefore choose our pivot so here
00:56:07
it is all quite indicated a so here we are
00:56:11
going to try to have heroes below
00:56:14
the pivot so here I already have 1 0 so
00:56:16
this line there will remain unchanged I will
00:56:19
therefore modified is what you can
00:56:21
see is what now I will therefore
00:56:24
modify line 2 isn't it and the
00:56:28
line between the nape of the neck so for line
00:56:32
2 what should you do you have to
00:56:34
do minus three times line a plus
00:56:39
line 2 is so there I would have minus
00:56:41
three plus three that will give me 0 for
00:56:44
line 4 so I'm going to do minus
00:56:47
twice line a plus the clear line and
00:56:53
I'm going to get
00:56:54
I'm going to get a system a
00:56:57
table the equivalent table following the
00:56:59
first line is unchanged so at -3 2
00:57:06
- 1 - 3 then minus three plus three that
00:57:14
makes zero that's the only goal 9.9 minus
00:57:20
three per month and 3.9 new ones +1 10 years 8
00:57:25
- 6 + 2 that makes minus 4 then plus that
00:57:33
3 + 0
00:57:36
that makes plus 3 and finally minus three by
00:57:40
-3 made + 9 + 9 + 11
00:57:44
that makes plus 20 the third line is
00:57:52
unchanged so I copy it such as 0
00:57:55
2 - 5 1 - 7
00:58:00
I modify my 4th and kouadio
00:58:04
by doing less twice l1 + l2 so
00:58:09
there I would necessarily have 0 and there that
00:58:12
will make me less than l - not less than
00:58:16
three it makes more 6 6 - people it makes
00:58:21
five years follows - from a - 4 + 3
00:58:31
I repeat - 4 + 3
00:58:34
that makes me minus a year following - 2nd +2
00:58:40
plus that makes three years 8 + 6 + 13 that
00:58:49
makes 19
00:58:50
I'm going just here so it turns out to
00:58:54
correspond well now here you
00:59:00
still have of course to choose the pivot
00:59:03
on my second line since
00:59:05
you call the objective is to
00:59:06
end with a system how I will
00:59:09
not repeat to you enough with a
00:59:11
triangular system the four unknowns then
00:59:14
the 3
00:59:15
then the two and then an unknown
00:59:18
so there I have my four unknowns there I have
00:59:21
more than 3 and 3 and 3 so they are
00:59:23
eliminating another one here suggests you
00:59:27
make a small modification
00:59:29
I have the choice between having a pivot equal
00:59:32
to 10 or if I lose mutz and line it
00:59:35
will make me a pivot equal to two that's what
00:59:37
I'm going to do I prefer to have a
00:59:38
pivot equal to 2 division by 2 is
00:59:41
more appropriate than division by ten
00:59:42
this being the case I can take advantage of it to
00:59:45
simplify this line if I
00:59:47
simplify it by two but I can't do it
00:59:49
since I have an odd number here
00:59:51
so I kept the line unchanged but
00:59:53
I could actually have done a half
00:59:55
of l2 n 2 you change to 2002 m but I
01:00:01
succeed in it so I'm going to
01:00:02
invert l2
01:00:04
and l3 so here l2 and l3 inverted I will
01:00:11
therefore have a table a system
01:00:13
equivalent to the following systems 1 - 3
01:00:18
less and less 3 years 8 0 in Parma 0-2
01:00:26
appointment we invert -5 1 - 7
01:00:33
lower 0 10 - 4 3 and 20 finally Madeira
01:00:42
equation which is unchanged 05 - with three
01:00:50
editions
01:00:52
I am now choosing my
01:00:54
pivot and we have no choice
01:00:56
the pivot will be two so we will have to
01:00:59
modify line 3 and line 4
01:01:04
ok so what operation will have to be seen
01:01:07
so from zero here geslin +2 the aged
01:01:11
plus swimming in addition said so I do
01:01:13
minus five times of this fact points 10
01:01:15
so I do minus 5 hands one no minus
01:01:19
five years in l2
01:01:20
plus they three that I will therefore be minus
01:01:22
a factory disk here we must have here 0
01:01:26
the g2 I do 2 / 2 that makes an x ​​- 5
01:01:31
so I will multiply the first here
01:01:33
by -5 2 me -5 2 a thousand times two that makes
01:01:37
minus 5
01:01:38
-5 then what did it do when I make
01:01:40
minus five half of l2 or more it 4.5
01:01:47
half shade hussein
01:01:48
I reproduce do I have space
01:01:51
yes I will reproduce in my next table
01:01:54
I copy my first line 1 - 3 2 - 1
01:02:01
then
01:02:03
3 my second says that I could
01:02:06
actually have divided by two I
01:02:08
'm going to leave I'm going to simply find
01:02:10
a normal scaled system
01:02:12
I don't want to reduce so two minus 5
01:02:16
ha ha and -7 and now we're going to
01:02:21
carry out the two remaining operations
01:02:23
so obviously you understood
01:02:24
there I will have 0 and there I will have 0 there is no
01:02:28
problem can check it by applying
01:02:30
this formula there you will find the same
01:02:32
value as here so for I place myself on
01:02:37
the city of Troyes so I do less 5
01:02:39
l 1:50 p.m. cusi that's 0 - 5 per month 5 +
01:02:45
25 + 25 - 4 + 25 - 4 + 21 so be
01:02:52
careful here of course - 10 chips 10-0
01:02:57
us + 25 - 4 + 21 so be careful - 5 +
01:03:05
3 - 5 + 3 agree - 5 inches too much is
01:03:10
less than then -5 l2 +35 +35 +20
01:03:27
+35 +20 +55 at the end of the year connects -5 2 to me
01:03:37
or 2 dry months of a thousand times that
01:03:40
is minus five months 5 + 5 that's zero
01:03:42
so be careful here -5 2 me by -5 that
01:03:48
's twenty-five half 25.2 me -25 half -
01:03:54
half 25.2 minus me by half that's 23
01:03:57
half that's our admitted next -5 2 me
01:04:05
plus three months 5.2 me +6 half that's
01:04:10
a half -5 2 me +6 half that's a half
01:04:17
then minus 7 by -5 2 me that's 35.2
01:04:23
me 35.2 me + 19 35 half plus 38 2 for me that's
01:04:31
seventy-three 2073 of life so
01:04:41
I'm going to if you would like to
01:04:43
resume my calculations
01:04:45
here I'm going to keep the easy ones because just
01:04:49
now I have a ferry calculation
01:04:51
having erased we can't come back
01:04:53
again once the advantage of having
01:04:54
everything take place all and all these
01:04:57
operations
01:04:58
it allows you to go back if
01:05:00
you ever notice at any given moment an
01:05:02
error of agreement you can always
01:05:04
go back on your calculations since everything is
01:05:06
recorded so here that is what I am going
01:05:08
to make travel 2 2 and 2 I am
01:05:11
simply going to say here which transforms
01:05:13
line 4 into twice twice twice it
01:05:17
because which will therefore give me an
01:05:21
equivalent system that I bring to you here
01:05:23
so here we go so at minus 3
01:05:29
I copy here 2 - 1
01:05:33
then 02 - 5 1
01:05:43
so here I have my in matrix which
01:05:47
is over there on the other side I have the
01:05:50
world on the right so minus 3d -7 then
01:05:55
here it is zero because it is
01:05:58
unchanged 0.21 -2 and 55
01:06:06
finally I multiplied everything by two so that
01:06:10
gives me 00 23 ha and 73 okay
01:06:29
ok so I will be able now if
01:06:31
you want I will delete here
01:06:33
agreement I'm going to go from leaving and I
01:06:37
'm going to so I'm going to here I'm going to
01:06:42
here therefore performed an operation on line
01:06:45
4 a hungry in order to have a zero here I
01:06:51
'm therefore going to perform an operation on
01:06:53
line 4 in order to have a zero here so I
01:06:56
'm going to do what
01:06:57
I'm going to multiply I'm going to so of course
01:06:59
my pivot
01:07:01
I should have said the pivot this time
01:07:03
it's how much 21 excuse me a little
01:07:06
foot is worth 7 21 so I have to have
01:07:08
1-0 below the peak so I'm going to
01:07:11
multi divide its part 21 and
01:07:36
must have 23 it's less than 23
01:07:39
months 23 + 23 5 0 so I'm going to reproduce
01:07:42
on the board here so my first line
01:07:45
remains unchanged so 1 - 3 2 - 1 - 3 02 -
01:07:58
5 1
01:08:00
- then 00 21 - 2 55
01:08:12
so there we said that Navarre 00 there
01:08:16
I will necessarily have 0 why I would have
01:08:19
zero because 21 / 21 times at least 23
01:08:23
points 3 that's zero so here I'm going to
01:08:27
do minus twenty three times minus two
01:08:31
that's plus 46
01:08:33
46 over 46 over 21 is
01:08:37
n't it forty six 46 over 21
01:08:43
lower 46 46 over 21 46 of course 46 over 21
01:08:51
years I write minus twenty three times negative
01:08:55
two so that 's 46 46 over 21 higher
01:09:03
that is to say + 21 of which 46 +21 that makes
01:09:09
so do I have yes 46 knox did
01:09:16
67 46 +21 over 21
01:09:20
that makes sixty this 21st so here 67
01:09:25
over 21 okay when I repeat myself
01:09:31
23/21 times minus two that makes 46 21st +1
01:09:36
21 on 21
01:09:38
that's 60 7 on 21 now you have to
01:09:42
do what you have to do so minus 23 50 - 23 on
01:09:49
21 that multiplies 55 + 73
01:09:56
so I leave you the operation there I
01:09:59
think that after calculation it must make 267
01:10:04
operation so here you do after x
01:10:06
21 over 21 does the whole operation
01:10:10
and that should give you 268 over 21 260 8
01:10:20
over 21 - 23 x 55 + 73 x 21 is
01:10:26
simply equal to 260 8 over 21 well
01:10:32
[Music]
01:10:34
so there you you understood that my
01:10:36
last line I can almost write
01:10:39
instead instead I see very clearly
01:10:42
that the 21 is going to disappear and I see very
01:10:45
clearly that 67
01:10:46
well I'm going to write it like that so
01:10:49
instead of n 4
01:10:50
I'm going to write quite simply quite
01:10:54
simply I'm going to multiply both
01:10:56
members by 21 over 67
01:11:02
why I say that because I see that
01:11:05
268 and a multiple of 67 4 x 67 equals
01:11:12
268
01:11:13
so I'm going to obtain the table the
01:11:17
system scales the following so I
01:11:20
'm going to copy or that I am going to copy
01:11:23
here that there I copied so here to the
01:11:31
ball to what I obtain I therefore obtain
01:11:33
1 - 3 2 - 1 - 3 02 - 5 1 - 7 years 8 00 21
01:11:57
less than 55 and by carrying out our
01:12:02
operation 000 here I'm going to get one
01:12:08
since I have
01:12:22
draw so been equal 4
01:12:27
then 21 y 21 years 21 n 21 z
01:12:37
21 z - of tea equals 55 years 8 2 2 y
01:12:52
- 5z plus you are b win minus 7 and
01:13:01
finally my first equation x -3 y plus
01:13:07
z - was also a hole then I
01:13:13
just have to replace in a
01:13:15
successive way then we were
01:13:19
equal 4
01:13:20
I replace t by four here minus
01:13:25
twice 4 that's minus 8 - 8 that I pass
01:13:29
to the other side that's plus 8
01:13:31
that makes 55 55 + 8 that makes 63
01:13:37
that makes 21 help equals 63 21 help I
01:13:43
write it 6.21 help equal 63 so n is
01:13:48
indeed equal to 60 3 over 21
01:13:50
that is to say z is simply equal
01:13:53
to 3 z is equal to 3 that makes me here - 4 -
01:13:59
15 + 4 that makes minus 11 - 15 + 4 that makes
01:14:04
less to the minuses that I carry on
01:14:06
our side that makes plus 11 11 - 7 11 - 7
01:14:13
that makes 4 2 y legal 4 that is to say
01:14:17
yak-42 y equals 2 you understood that at 3
01:14:21
2 inevitably I will find x and win
01:14:23
when I arranged for the
01:14:25
answer to be ten easy matches so that
01:14:27
makes me here - 6 why because two
01:14:30
- three times minus 6 +6 that makes 0 0 -
01:14:37
4 - 4 that I doors on the other side
01:14:40
on
01:14:41
4 - 4 + 4 - 3 that makes x also the
01:14:47
solution of my system
01:14:49
that's all simply the quadruplet at
01:14:52
two three or four you just had to
01:14:57
guess it so the problem is that with this
01:15:02
system I had started a
01:15:04
talent calculation which I had to erase because
01:15:05
I must have made an operation error
01:15:07
so I had to do all the calculations by
01:15:09
hand to avoid the breeder
01:15:13
so apparently everything works so
01:15:16
I would have liked to actually extend
01:15:17
this sequence and show you how to
01:15:20
solve this system there by
01:15:24
always using the kids' pivot method
01:15:26
but instead instead of
01:15:28
determining a scaled system it was
01:15:32
trying to find what we call a
01:15:35
to end with what we call the
01:15:38
units matrix in other words we are going to
01:15:39
go through a matrix inversion at
01:15:41
the limit I in this case I am going to
01:15:43
keep this sequence there for the
01:15:45
next time since in the next round
01:15:47
we will therefore approach the calculation
01:15:49
matrix calculation so with all that is
01:15:53
operations on matrices
01:15:55
matrix inversion precisely in order to solve
01:15:57
this system these systems
01:16:02
of equations I had I 'had promised
01:16:05
I had planned to do this type
01:16:08
of exercise so it is a dcg exercise
01:16:12
good a system of equations to solve
01:16:15
but unfortunately I fear that I
01:16:18
will snap that I make time be a
01:16:20
party it is how much they two hours I
01:16:22
thought I would finish at 1 p.m. so here it is in
01:16:25
any case I hope that this sequence does
01:16:28
not go well and being too long
01:16:30
I tell you once again very soon
01:16:31
and then continue to follow her lessons
01:16:35
since she is address I'm trying to
01:16:37
build something truly
01:16:38
global so that everyone
01:16:41
can find what they're looking for, especially for
01:16:43
those who are preparing for studies,
01:16:45
so my economy of studies which are
01:16:50
in the accounting sector
01:16:52
and not all cases thank you for your
01:16:55
comments do not hesitate to come and read
01:16:58
his videos and then see you very soon
01:17:00
for the next one

Description:

SYSTÈMES LINÉAIRES. RÉSOLUTION PAR LA MÉTHODE DU PIVOT DE GAUSS. CFA ACE PARIS

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