Q98 / 180 · COMEDK 2014 · Mathematics

If $\left[\begin{array}{cc}-2 & 5 \\ 3 & -1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{cc}1 & 2 \\ 3 & 4\end{array}\right]\left[\begin{array}{c}3 \\ -1\end{array}\right]$, then $(x, y)$ is

  • A
    $(1,2)$
  • B
    $(-1,2$
  • C
    $(1,-2$
  • Correct answer
    D
    $(2,1)$

Solution

$\left[\begin{array}{cc}-2 & 5 \\ 3 & -1\end{array}\right]_{2 x \times 2}\left[\begin{array}{l}x \\ y\end{array}\right]_{2 \times 1}=\left[\begin{array}{cc}1 & 2 \\ 3 & 4\end{array}\right]_{2 \times 2}\left[\begin{array}{c}3 \\ -1\end{array}\right]_{2 \times 1}$ $\Rightarrow\left[\begin{array}{c}-2 x+5 y \\ 3 x-y\end{array}\right]=\left[\begin{array}{l}1 \\ 5\end{array}\right]$ $\Rightarrow-2 x+5 y=1,3 x-y=5$ or $y=3 x-5 \quad \text{...(i)}$ $\Rightarrow \quad-2 x+5(3 x-5)=1$ $\Rightarrow \quad-2 x+15 x-25=1$ $\Rightarrow \quad 13 x=26 \Rightarrow x=2$ Substituting $x=2$ in Eq. (i), we get $$ y=6-5=1 $$ Hence, $(x, y)=(2,1)$

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

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