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Question
If \[\binom{x + y}{x - y} = \begin{bmatrix}2 & 1 \\ 4 & 3\end{bmatrix}\binom{1}{ - 2}\] , then write the value of (x, y).
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Solution
\[\binom{x + y}{x - y} = \begin{bmatrix}2 & 1 \\ 4 & 3\end{bmatrix}\binom{1}{ - 2}\]
\[ \Rightarrow \binom{x + y}{x - y} = \binom{2 - 2}{4 - 6}\]
\[ \Rightarrow \binom{x + y}{x - y} = \binom{0}{ - 2}\]
Corresponding elements of equal matrices are equal.
\[ \therefore x + y = \text{0 and }x - y = - 2\]
\[ \Rightarrow x = \text{- y and } - y - y = - 2\]
\[ \Rightarrow x =\text{ - y and } y = 1\]
\[ \Rightarrow x =\text{ - 1 and } y = 1\]
\[Hence, (x, y) = \left( - 1, 1 \right) .\]
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