Question:
For what values of x and y are the following matrices equal?
$A=\left[\begin{array}{cc}2 x+1 & 2 y \\ 0 & y^{2}-5 y\end{array}\right], B=\left[\begin{array}{cc}x+3 & y^{2}+2 \\ 0 & -6\end{array}\right]$
Solution:
As the given matrices A and B are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get
$2 x+1=x+3 \quad 2 y=y^{2}+2$
$\begin{array}{ll}0=0 & y^{2}-5 y=-6\end{array}$
On simplifying, we get
$x=2$, but there is no common value of $y$ for which $A$ and $B$ are equal.
Hence, A and B cannot be equal for any value of y.