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प्रश्न
If \[2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] , find x − y.
उत्तर
\[2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}6 + 1 & 8 + y \\ 10 + 0 & 2x + 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}7 & 8 + y \\ 10 & 2x + 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\]
\[ \Rightarrow 8 + y =\text{ 0 and }2x + 1 = 5\]
\[ \Rightarrow y =\text{- 8 and } 2x = 4\]
\[ \Rightarrow y =\text{ - 8 and } x = 2\]
\[Hence, x - y = 2 - ( - 8) = 10 .\]
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