If find A^–1. Using A^–1, solve the system of linear equations x – 2y = 10, 2x – y – z = 8, –2y + z = 7.

We have,

We have to find A^-1 and

Firstly, we find |A|

Expanding |A| along C₁, we get

= (-1 + 2) + 2 (0) + 0

= 1

Now, we have to find adj A and for that we have to find co-factors:

Now, the system of linear equation is

x – 2y = 10

2x – y – z = 8

-2y + z = 7

We know that, AX = B

Here,

and we can see that this matrix is the transpose of the given matrix. So, transpose of A^-1 is

⇒ X = A^-1B

∴ x = 0, y = -5 and z = -3