Q102 / 180 · KCET 2018 · Mathematics

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
    \( 3,1 \)
  • Correct answer
    D
    \( -1,3 \)

Solution

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 \( x=-1, y=3 \)

Hence, the correct answer is option: 'D'.

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