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Question:

If $\left[\begin{array}{cc}x y & 4 \\ z+6 & x+y\end{array}\right]=\left[\begin{array}{ll}8 & w \\ 0 & 6\end{array}\right]$, write the value of $(x+y+z)$

Solution:

$\left[\begin{array}{cc}x y & 4 \\ z+6 & x+y\end{array}\right]=\left[\begin{array}{ll}8 & w \\ 0 & 6\end{array}\right]$

Corresponding elements of equal matrices are equal.

$\therefore z+6=0 \quad$ and $\quad x+y=6$

$\Rightarrow z=-6 \quad$ and $\quad x+y=6$

Therefore, $x+y+z=6-6=0$.

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