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this is a system of equations that we used in one of the earlier the listed
illustrate
the use of raw rations
and the row operations to to solve the system
i want to mail use the same system telestrator the connection with matrix n
verses
and also to illustrate use of the matrix to to calculate a matrix inverse
so now we switch over to the matrix to and i'm going to name a matrix capital c
which will be the coefficient matrix of that system it was explosive live plus
four c
in the first equation one x one y foresee
the second equation there was no next term it was too wide
and five c
and in the third equation has three xd two y
and foresee
so capital sees my coefficient matrix and the numbers on the right
i'm going to put into a
column which i'll call lower case b
and the first equation that was two on the right
in the second equation it was four and a thirty question it was minus seven
so let's check and make sure the matrix to understands these matrices of entered
capital c
looks right
lower case b
looks right
what we've seen is that you can solve a system of the equation
spelled equations if you take the embers of the coefficient matrix and multiplied
times that column of numbers
the inverse of the coefficient matrix
can be calculated in the matrix to a seat to the power of these little care
assemble for power
an exponent minus one
and we want to multiply that times
lower case b day so weird calculating the inverse of that freed up three
matrix c
the inverse will be three by three
and we're more point multiply that inverse times a column b_ and that
should give us the solutions
for x_ y_ and z_ in the system of equations let's do it
what we get his ex equals minus three michael's minus three sequels to you
check that indeed that does solve the system of equations