SOLUTION: Solve the systems using the inverse matrix method: 5. {-3x + 9y = 9 { 3x + 2y = 13 6. { x + 2y + 3z = =8 { x + y + z = -11 {2x + 2y + z = -2 Please

Question 965591: Solve the systems using the inverse matrix method:
5. {-3x + 9y = 9
{ 3x + 2y = 13

6. { x + 2y + 3z = =8
{ x + y + z = -11
{2x + 2y + z = -2
Please help! I am so lost on how to set these up. Please show work so I can follow along. Thank you so much!
Answer by hkwu(60) (Show Source): You can put this solution on YOUR website!
I won't solve for this because it's tedious and you should be doing it yourself. The idea is to notice that if A is an invertible matrix, then

is equivalent to

Thus, if you find

then you can solve for

easily by multiplying

on the left by

.
In case you don't know how to find the inverse of a matrix: write the coefficient matrix down and augment the other side of the matrix with the

identity matrix. Row reduce to reduced row echelon form on the left side. The right matrix will then be the inverse for the original matrix.
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Leave a message if I helped.
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