solve the matrix equation for x

Question

solve the matrix equation for x

x[ -1 0 1

1 1 0

3 1 -1 ]

=

[1 3 0

-7 1 10

]

Answer 1

If we name the matrix that multiples x A and the result B, our equation is:

xA = B

If you multiply both sides by the inverse of A, you get:

xAA^-1 = BA^-1

A matrix multiplied by its inverse yields the identity matrix, so the equation becomes:

x = BA^-1

In order to solve this equation, you need to find the inverse of the matrix that multiplies x. This inverse is:

A^-1 = [1 −1 1

−1 2 −1

2 −1 1]

So:

x = [1 3 0

-7 1 10]

*

[1 −1 1

−1 2 −1

2 −1 1]

x = [−2 5 −2

12 −1 2]