Question

If $\left[\begin{array}{cc}xy& 4\\ z+6& x+y\end{array}\right]=\left[\begin{array}{cc}8& w\\ 0& 6\end{array}\right]$ then find values of $x,y,z\text{and}w$.

Answer 1

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

By comparing corresponding elements, we get

$x+y=6$ ....(1)

$xy=8$ ....(2)

$z+6=0\Rightarrow z=-6$
and $w=4$

Solve equations (1) and (2) to get the value of $x\text{and}y$

Substituting $x=6-y$ from eq.(1) in (2)

$(6-y)y=8$
$\Rightarrow y^2-6y+8=0$

$\Rightarrow (y-2)(y-4)=0$

$\Rightarrow y=2\text{or}y=4$

$\Rightarrow x=4\text{or}x=2$

[ On Putting value of 𝑦 in equation (1) ]
Hence, the values are
$x=2,y=4\text{or}x=4,y=2,z=-6\text{and}w=4$