Question

If $(\begin{array}{cc}1& 2\\ 2& 1\end{array})(\begin{array}{c}x\\ y\end{array})=(\begin{array}{c}2\\ 4\end{array})$, then the values of $x$ and $y$ respectively, are

• A. $2,0$
• B. $0,2$
• C. $0,-2$
• D. $1,1$

Answer 1

The correct option is A $2,0$

$\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}2\\ 4\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}x& 2y\\ 2x& y\end{array}\right]=\left[\begin{array}{c}2\\ 4\end{array}\right]$

$\Rightarrow x+2y=2⟶\left(1\right)\&2x+y=4⟶\left(2\right)$

Multiply $\left(1\right)$ by 2,$

$\Rightarrow 2x+4y=4⟶\left(3\right)$

Solving $\left(2\right)\&\left(3\right),\left[\right(2)-(3\left)\right],$ we get

$\Rightarrow -3y=0$

$\Rightarrow y=0$

Put $y=0$ in $\left(1\right),$ we get

$\Rightarrow x+0=2$

$\Rightarrow x=2$

$\Rightarrow y=0$

Hence, the answer is $2,0.$