# Which of the given values of x and y make the following pair of matrices equal

Question:

Which of the given values of x and y make the following pair of matrices equal

$\left[\begin{array}{ll}3 x+7 & 5 \\ y+1 & 2-3 x\end{array}\right]=\left[\begin{array}{ll}0 & y-2 \\ 8 & 4\end{array}\right]$

(A) $x=\frac{-1}{3}, y=7$

(B) Not possible to find

(C) $y=7, x=\frac{-2}{3}$

(D) $x=\frac{-1}{3}, y=\frac{-2}{3}$

Solution:

The correct answer is B.

It is given that $\left[\begin{array}{ll}3 x+7 & 5 \\ y+1 & 2-3 x\end{array}\right]=\left[\begin{array}{ll}0 & y-2 \\ 8 & 4\end{array}\right]$

Equating the corresponding elements, we get:

$3 x+7=0 \Rightarrow x=-\frac{7}{3}$

$5=y-2 \Rightarrow y=7$

$y+1=8 \Rightarrow y=7$

$2-3 x=4 \Rightarrow x=-\frac{2}{3}$

We find that on comparing the corresponding elements of the two matrices, we get two different values of x, which is not possible.

Hence, it is not possible to find the values of x and y for which the given matrices are equal.