For what values of `x` and `y` are the following matrices equal? `A=[(2x+1, 3y),(0,y^2-5y)]` , `B=[(x+3,y^2+2),( 0,-6)]`

Explanation

To find the values of \( x \) and \( y \) for which the matrices \( A \) and \( B \) are equal, we need to equate the corresponding elements of both matrices.

Given:
\[ A = \begin{pmatrix} 2x + 1 & 3y \\ 0 & y^2 - 5y \end{pmatrix} \]
\[ B = \begin{pmatrix} x + 3 & y^2 + 2 \\ 0 & -6 \end{pmatrix} \]

Since both matrices are \( 2 \times 2 \), we can equate their corresponding elements:

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