Mathematics

Problem

Let

X

and

Y

be matrices of order

2\times2

satisfying the simultaneous matrix equations

3X-2Y=\begin{bmatrix}7&-1\\10&4\end{bmatrix},\qquad 4X+Y=\begin{bmatrix}5&8\\-2&6\end{bmatrix}.

(a) Express

Y

in terms of

X

using the first equation. (b) Substitute the expression for

Y

into the second equation and solve for

X

. (c) Hence obtain the matrix

Y