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Question
If \[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\]
Options
x = 3 , y =-1
x = 2 , y= 3
x= 2 , y= 4
x = 3, y= 3
Solution
\[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\]
Corresponding elements of equal matrices are equal .
\[ \therefore 4x = \text{x + 6 and 2x + y} = 7\]
\[ \Rightarrow 3x = \text{6 and 2x + y} = 7\]
\[ \Rightarrow x = \text{2 and 2x + y }= 7\]
\[ \Rightarrow x = \text{2 and 2 ×2 + y }= 7\]
\[ \Rightarrow x = \text{2 and y } =7 - 4\]
\[ \Rightarrow x = \text{2 and y} = 3\]
Therefore, x = 2, y = 3.
Hence, the correct option is (b).
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