KCET · Maths · Matrices
If \( \left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y}\end{array}\right]=\left[\begin{array}{c}2 \\ 4\end{array}\right] \), then the values of \( \mathrm{x} \) and \( \mathrm{y} \) respectively are
- A \( -3,-1 \)
- B \( 1,3 \)
- C \( 3,1 \)
- D \( -1,3 \)
Answer & Solution
Correct Answer
(D) \( -1,3 \)
Step-by-step Solution
Detailed explanation
Given that, \( \left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right] \)
\( \left[\begin{array}{c}x+y \\ -x+y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right] \)
So, \( x+y=2 \rightarrow \) (1)
and \( -x+y=4 \rightarrow(2) \)
From Eqs. (1) and (2), we have \( x=-1, y=3 \)
\( \left[\begin{array}{c}x+y \\ -x+y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right] \)
So, \( x+y=2 \rightarrow \) (1)
and \( -x+y=4 \rightarrow(2) \)
From Eqs. (1) and (2), we have \( x=-1, y=3 \)
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