If $\begin{bmatrix}x+y&4\\1+z&y\end{bmatrix}=\begin{bmatrix}2&4\\5&6\end{bmatrix}$, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $x=-4, y=6,z= 4$
Given:
$\begin{pmatrix}x+y & 4 \\ 1+z & y\end{pmatrix} =\begin{pmatrix}2 & 4 \\ 5 & 6\end{pmatrix}$
Equate corresponding entries:
$x+y=2$
$4=4$ (always true)
$1+z=5\Rightarrow z=4$
$y=6$
Now substitute $y=6$ into $x+y=2$:
$x+6=2\Rightarrow x=-4$
Thus $x=-4,\;y=6,\;z=4$.