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 the values of x, y, z 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 equality of matrix, x + y = 6 and xy = 8

$\Rightarrow$ x = 6 - y and (6 - y). y = 8

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

$\Rightarrow$ $y^2$ - 4y-2y+8=0

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

$\Rightarrow$ y = 2 or y = 4

$\therefore$ x = 6 - 2 = 4

or x = 6 - 4 = 2

Also, z + 6 = 0

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

$\therefore$ x = 2, y = 4 or x = 4, y = 2 , z = - -6 and w = 4