SOLUTION: Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B) x+8y=-29 6x+2y=10

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Question 122173This question is from textbook
: Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B)
x+8y=-29
6x+2y=10 This question is from textbook

Found 2 solutions by Edwin McCravy, moe jaberrr:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B) 
  x + 4y = 22
-6x + 5y = 13

Form the matrix equation:

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Now we must find the inverse of the coefficient matrix %28matrix%282%2C2%2C1%2C4%2C-6%2C5%29%29
To find the inverse of a 2x2 matrix:
1. find the determinant of the matrix:
abs%28matrix%282%2C2%2C1%2C4%2C-6%2C5%29%29%29=%281%29%285%29-%284%29%28-6%29=5%2B24=29
2. Swap the upper left and lower right elements
%28matrix%282%2C2%2C5%2C4%2C-6%2C1%29%29
3. Change the signs of the upper right and lower left elements
%28matrix%282%2C2%2C5%2C-4%2C6%2C1%29%29
4. Divide every term by the value of the determinant, which is 29.
%28matrix%282%2C2%2C5%2F29%2C-4%2F29%2C6%2F29%2C1%2F29%29%29
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Now go back to the matrix equation

            

Multiply the inverse matrix on the left of the
left side and also on the left of the right side;



I assume you know how to multiply matrices. If you
don't, post again asking how to. Multiply the first
two matrices on the left, and multiply the matrices on
the right:

            

We have the identity matrix on the left to multiply by
the matrix %28matrix%282%2C1%2Cx%2Cy%29%29 which just gives:

                %28matrix%282%2C1%2Cx%2Cy%29%29=%28matrix%282%2C1%2C2%2C5%29%29

So we see that x = 2 and y = 5.

Edwin

Answer by moe jaberrr(1) About Me  (Show Source):