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).

 

Answer 1

\[\binom{x + y}{x - y} = \begin{bmatrix}2 & 1 \\ 4 & 3\end{bmatrix}\binom{1}{ - 2}\] 

\[ \Rightarrow \binom{x + y}{x - y} = \binom{2 - 2}{4 - 6}\] 

\[ \Rightarrow \binom{x + y}{x - y} = \binom{0}{ - 2}\] 

Corresponding elements of equal matrices are equal.

\[ \therefore x + y = \text{0 and }x - y = - 2\] 

\[ \Rightarrow x = \text{- y and } - y - y = - 2\] 

\[ \Rightarrow x =\text{ - y and } y = 1\] 

\[ \Rightarrow x =\text{ - 1 and } y = 1\] 

\[Hence, (x, y) = \left( - 1, 1 \right) .\]