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Question
Which of the given values of x and y make the following pairs of matrices equal? \[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix}, \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\]
Options
x =\[- \frac{1}{3}\],y = 7
y = 7, x = \[- \frac{2}{3}\]
x = \[- \frac{1}{3}\] 4 =\[- \frac{2}{5}\]
Not possible to find
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Solution
Not possible to find
\[Here, \]
\[\begin{bmatrix}3x + 7 & 5 \\ y + 1 & 2 - 3x\end{bmatrix} = \begin{bmatrix}0 & y - 2 \\ 8 & 4\end{bmatrix}\]
`"We know that for two equal matrices the corresponding elements are equal ."`
\[ \therefore 3x + 7 = 0, 5 = y - 2, y + 1 = \text{8 and 2 - 3x }= 4\]
\[ \Rightarrow 3x = - 7, 5 + 2 = y, y = \text{ 8 -1 and - 3x} = 4 - 2\]
\[ \Rightarrow x = \frac{- 7}{3}, y = 7, y = \text{7 and x} = - \frac{2}{3} \]
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