Question

Given 3\begin{bmatrix}x&y\\\z&w\end{bmatrix}$$=\begin{bmatrix}x&6\\\\-1&2w\end{bmatrix}+\begin{bmatrix}4& x+y\\\ z+w& 3\end{bmatrix},find the values of x,y,z and w

Answer 1

The correct answer is $x=2,y=4,z=1\space and\space w=3$
3\begin{bmatrix}x&y\\\z&w\end{bmatrix}$$=\begin{bmatrix}x&6\\\\-1&2w\end{bmatrix}+\begin{bmatrix}4& x+y\\\ z+w& 3\end{bmatrix}
$\implies\begin{bmatrix}3x& 3y\\\ 3z& 3w\end{bmatrix}=\begin{bmatrix}x+4& 6+x+y\\\ -1+z+w& 2w+3\end{bmatrix}$
Comparing the corresponding elements of these two matrices, we get:
$3x=x+4$
$\implies2x=4$
$\implies x=2$
$3y=6+x+y$
$\implies2y=6+x$
$\implies y=4$
$3w=2w+3$
$\implies w=3$
$3z=-1+z+w$
$\implies2z=-1+w$
$=-1+3$
$\implies z=1$
$\therefore x=2,y=4,z=1\space and\space w=3$