Question

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

$\left(a\right)x=\frac{-1}{3},y=7$
(b) Not possible to find
$\left(c\right)y=7,x=\frac{-2}{3}\left(d\right)x=\frac{-1}{3},y=\frac{-2}{3}$

Answer 1

According to the question, $\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right]=\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$
By defintion of equality of matrices, we have
3x+7=0 .......(i)
5=y-2 .......(ii)
y+1=8 .......(iii)
2-3x=4 .......(iv)
From Eq. (ii), y=7
From Eq. (i), $3x+7=0\Rightarrow x=\frac{-7}{3}$
From Eq. (iv), $2-3x=4\Rightarrow x=\frac{-2}{3}$
Since, x can have only one value at a time. Hence, it is not possible to find the values of x and y for which the given matrices are equal.
So, correct option is (b).
Note Sometimes on solving an equation, we get more than one values of the varialbes. This means that such a matrix does not exist.