Question

Which of the given values of $x$ and $y$ make the following pair of matrices equal.
$\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right]=\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$

• A. $x=\frac{-1}{3},y=7$
• B. Not possible to find
• C. $y=7,x=\frac{-2}{3}$
• D. $x=\frac{-1}{3},y=\frac{-2}{3}$

Answer 1

Answer: (B)

Not possible to find

$\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right]=\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$
Equating the corresponding elements, we get,
$3x+7=0\Rightarrow x=-\frac{7}{3}$
$5=y-2\Rightarrow y=7$
$y+1=8\Rightarrow y=7$
$2-3x=4\Rightarrow x=-\frac{2}{3}$
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.