Question

For what values of $x$ and $y$ are the following matrices equal?
$A=\left[\begin{array}{cc}2x+1& 3y\\ 0& y^2-5y\end{array}\right],B=\left[\begin{array}{cc}x+3& y^2+2\\ 0& -6\end{array}\right]$. Then $x-y=$

Answer 1

Given,
$A=\left[\begin{array}{cc}2x+1& 3y\\ 0& y^2-5y\end{array}\right],=\left[\begin{array}{cc}x+3& y^2+2\\ 0& -6\end{array}\right]$
Comparing the elements we have,
$\Rightarrow 2x+1=x+3$ ..... (1)
$3y=y^2+2$ ......... (2)
$y^2-5y=-6$ .......... (3)
$\Rightarrow x=2$ [From Eq. (1)]
$y=1$ or $2$ [From Eq. (2)]
$y=2$ or $3$ [From Eq. (3)]
$\Rightarrow x=2$ and $y=2$
Then $x-y$ $=0$