For what values of x and y are the following matrices equal?
$A=\begin{bmatrix}2x+1&3y\\0&y^2-5y\end{bmatrix},B=\begin{bmatrix}x+3&y^2+2\\0&-6\end{bmatrix}$.
Answer & explanation
Correct answer: option 1
We have,
$\begin{bmatrix}2x+1&3y\\0&y^2-5y\end{bmatrix}=\begin{bmatrix}x+3&y^2+2\\0&-6\end{bmatrix}$
$⇒2x+1=x+3$ ..... (1)
$3y=y^2+2$ ..... (2)
$y^2−5y=−6$ ..... (3)
$⇒x=2$ [From Eq. (1)]
$y=1\, or\, 2$ [From Eq. (2)]
$y=2\, or\, 3$ [From Eq. (3)]
So, $x = 2, y = 2$