Question

If $A=\left[\begin{array}{ccc}1& 2& x\\ 3& -1& 2\end{array}\right]$ and $B=\left[\begin{array}{c}y\\ x\\ 1\end{array}\right]$ be such that $AB=\left[\begin{array}{c}6\\ 8\end{array}\right]$, then :

• A. $y=2x$
• B. $y=-2x$
• C. $y=x$
• D. $y=-x$

Answer 1

Answer: (A)

$y=2x$

$AB=\left[\begin{array}{c}6\\ 8\end{array}\right]$

$\left[\begin{array}{ccc}1& 2& x\\ 3& -1& 2\end{array}\right]\left[\begin{array}{c}y\\ x\\ 1\end{array}\right]=\left[\begin{array}{c}6\\ 8\end{array}\right]$

$\left[\begin{array}{c}y+3x\\ -x+3y+2\end{array}\right]=\left[\begin{array}{c}6\\ 8\end{array}\right]$ .

$\Rightarrow y+3x=6$ and $-x+3y=6$

Subtract the equations $4x-2y=0$

$\Rightarrow y=2x$