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

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Question:

Which of the given values of $x$ and $y$ make the following pairs of matrices equal?

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

(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

Solution:

(d) Not possible to find

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

We know that for two equal matrice $s$ the corresponding elements are equal.

$\therefore 3 x+7=0,5=y-2, y+1=8$ and $2-3 x=4$

$\Rightarrow 3 x=-7,5+2=y, y=8-1$ and $-3 x=4-2$

$\Rightarrow x=\frac{-7}{3}, y=7, y=7$ and $x=-\frac{2}{3}$

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