For what values of x and y are the following matrices equal?


For what values of x and y are the following matrices equal?

$A=\left[\begin{array}{cc}2 x+1 & 2 y \\ 0 & y^{2}-5 y\end{array}\right], B=\left[\begin{array}{cc}x+3 & y^{2}+2 \\ 0 & -6\end{array}\right]$


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.

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