Question

Solve the equation for x,y,z and t if 2$\begin{bmatrix}x&y\\\y&t\end{bmatrix}$+3$\begin{bmatrix}1&-1\\\0&2\end{bmatrix}$=3$\begin{bmatrix}3&5\\\4&6\end{bmatrix}$

Answer 1

2$\begin{bmatrix}x&y\\\y&t\end{bmatrix}$+3$\begin{bmatrix}1&-1\\\0&2\end{bmatrix}$=3$\begin{bmatrix}3&5\\\4&6\end{bmatrix}$

$\Rightarrow$ $\begin{bmatrix}2x&2z\\\2y&2t\end{bmatrix}$+$\begin{bmatrix}3&-3\\\0&6\end{bmatrix}$=$\begin{bmatrix}9&15\\\12&18\end{bmatrix}$

$\Rightarrow \begin{bmatrix}2x+3&2z-3\\\2y&2t+6\end{bmatrix}$=$\begin{bmatrix}9&15\\\12&18\end{bmatrix}$
Comparing the corresponding elements of these two matrices, we get:
2x+3=9
$\Rightarrow$ x=3
2y=12
$\Rightarrow$ y=6
2z-3=15
$\Rightarrow$ 2z=18
z=9
2t+6=18
2t=12
t=6.

$\therefore$ x=3,y=6,z=9 and t=6