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)

Let $A=\left[\begin{array}{ccc}1& 2& x\\ 3& -1& 2\end{array}\right]$ and $B=\left[\begin{array}{c}y\\ x\\ 1\end{array}\right]$
$AB=\left[\begin{array}{ccc}1& 2& x\\ 3& -1& 2\end{array}\right]\left[\begin{array}{c}y\\ x\\ 1\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}6\\ 8\end{array}\right]=\left[\begin{array}{c}y+2x+x\\ 3y-x+2\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}6\\ 8\end{array}\right]=\left[\begin{array}{c}y+3x\\ 3y-x+2\end{array}\right]$
$\Rightarrow y+3x=6$ and $3y-x=6$
On solving, we get
$x=\frac{6}{5}$ and $y=\frac{12}{5}$
$\Rightarrow y=2x$