Question

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

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

Answer 1

​As the given matrices A and B are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get

2x + 1 = x + 3 2y = y² + 2
0 = 0 y² − 5y = −6

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.