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
To find the inverse of a 2x2 matrix:
1. find the determinant of the matrix:
=
2. Swap the upper left and lower right elements
3. Change the signs of the upper right and lower left elements
4. Divide every term by the value of the determinant, which is 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 which just gives:
So we see that x = 2 and y = 5.
Edwin