If $2x – y =\begin{bmatrix}3&-3&0\\3&3&2\end{bmatrix}$ and $2y + x =\begin{bmatrix}4&1&5\\-1&4&-4\end{bmatrix}$, then
Answer & explanation
Correct answer: option 2
$∵2x – y =\begin{bmatrix}3&-3&0\\3&3&2\end{bmatrix}$ ...(i)
$⇒4x – 2y =\begin{bmatrix}6&-6&0\\6&6&4\end{bmatrix}$ ...(ii)
and $x+2y=\begin{bmatrix}4&1&5\\-1&4&-4\end{bmatrix}$ ....(iii)
Adding Eqs. (ii) and (iii), then
$5x=\begin{bmatrix}10&-5&5\\5&10&0\end{bmatrix}$ $∴x=\begin{bmatrix}2&-1&1\\1&2&0\end{bmatrix}$
From Eq. (iii), $2x+4y =\begin{bmatrix}8&2&10\\-2&8&-8\end{bmatrix}$ ....(iv)
Substracting Eq. (i) from (iv), then
$5y=\begin{bmatrix}5&5&10\\-5&5&-10\end{bmatrix}$ $∴\begin{bmatrix}1&1&2\\-1&1&-2\end{bmatrix}$