Question

If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y

2X + 3Y = \(\begin{bmatrix} 2 & 3 \\[0.3em] 4 & 0 \end{bmatrix}\), 3X + 2Y = \(\begin{bmatrix} -2 & 2 \\[0.3em] 1 & -5 \end{bmatrix}\)

Answer 1

We have the matrix equations,

Adding equations (i) and (ii), we get

Adding equations (iii) and (iv), we get

Putting the matrix A in equation (iv), we get