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Question
If \[\begin{bmatrix}x & x - y \\ 2x + y & 7\end{bmatrix} = \begin{bmatrix}3 & 1 \\ 8 & 7\end{bmatrix}\] , then find the value of y.
Sum
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Solution
\[\text{We have}, \left[ \begin{array} "x & x - y \\ 2x + y & 7\end{array} \right] = \begin{bmatrix}3 & 1 \\ 8 & 7\end{bmatrix}\]
The corresponding elements of two equal matrices are equal .
\[ \therefore x = 3 \]
\[ x - y = 1 . . . \left( 1 \right) \]
Putting the value of x in eq . (1)
\[3 - y = 1\]
\[ \Rightarrow 3 - 1 = y\]
\[ \therefore y = 2\]
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