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Question
Find the value of x, if \[\begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]
Solution
The corresponding elements of two equal matrices are equal.
\[Given: \hspace{0.167em} \begin{bmatrix}3x + y & - y \\ 2y - x & 3\end{bmatrix} = \begin{bmatrix}1 & 2 \\ - 5 & 3\end{bmatrix}\]
\[3x + y = 1 . . . \left( 1 \right) \]
\[ - y = 2\]
\[ \Rightarrow y = - 2\]
Putting the value of y in eq .( 1 )
\[3x + \left( - 2 \right) = 1\]
\[ \Rightarrow 3x - 2 = 1\]
\[ \Rightarrow 3x = 1 + 2\]
\[ \Rightarrow 3x = 3\]
\[ \Rightarrow x = \frac{3}{3} = 1\]
\[ \therefore x = 1\]
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