Question

Find the inverse matrix of matrix \(\begin{bmatrix}1&-1&1\\[0.3em]2&1&-3\\[0.3em]1&1&1\end{bmatrix}\) and with the help of it, solve the following system of equations :

Answer 1

 Given  \(\begin{bmatrix}1&-1&1\\[0.3em]2&1&-3\\[0.3em]1&1&1\end{bmatrix}\) 

= 1(1 + 3) + 1(2 + 3) + 1(2 – 1)

= 4 + 5 + 1 = 10 ≠ 0

So, A^{– 1} exists.

On finding adjoint of A,

Matrix formed by adjoint of A,

Matrix form of equations