Question

Which of the given values of x and y make the following pairs of matrices equal?
$\left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right],\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$
(a) x = $-\frac{1}{3}$, y = 7
(b) y = 7, x = $-\frac{2}{3}$
(c) x = $-\frac{1}{3}$, 4 = $-\frac{2}{5}$
(d) Not possible to find

Answer 1

(d) Not possible to find


$$\begin{gathered} \mathrm{Here}, \\ \left[\begin{array}{cc}3x+7& 5\\ y+1& 2-3x\end{array}\right]=\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right] \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{for}\mathrm{two}\mathrm{equal}\mathrm{matrice}s\mathrm{the}\mathrm{corresponding}\mathrm{elements}\mathrm{are}\mathrm{equal}. \\ \therefore 3x+7=0,5=y-2,y+1=8\mathrm{and}2-3x=4 \\ \Rightarrow 3x=-7,5+2=y,y=8-1\mathrm{and}-3x=4-2 \\ \Rightarrow x=\frac{-7}{3},y=7,y=7\mathrm{and}x=-\frac{2}{3} \end{gathered}$$