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Which of the given values of x and y make the following pair of matrices equal [3x = 7 5 y = 1 2 - 3x], [0 y - 2 8 4] (A) x = - 1 / 3, y = 7 (B) not possible to find (C) y = 7, x = - 2 / 3 (D) x = -1/3, y = - 2/3

Q9.    Which of the given values of x and y make the following pair of matrices equal

 \begin{bmatrix} 3x + 7 &5 \\ y + 1 & 2 -3x \end{bmatrix}\begin{bmatrix} 0 & y - 2 \\ 8 & 4 \end{bmatrix}

        (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}

Answers (1)
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Given,     \begin{bmatrix} 3x + 7 &5 \\ y + 1 & 2 -3x \end{bmatrix} =\begin{bmatrix} 0 & y - 2 \\ 8 & 4 \end{bmatrix}

If two matrices are equal, then their corresponding elements are also equal

3x+7=0\Rightarrow x=\frac{-7}{3}   

 y-2=5 \Rightarrow y=5+2=7

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

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

Here, the value of x is not unique, so option B is correct.

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