Question

The value of $x$ such that $\left[\begin{array}{ccc}1& 2& 1\end{array}\right]\left[\begin{array}{ccc}1& 2& 0\\ 2& 0& 1\\ 1& 0& 2\end{array}\right]\left[\begin{array}{c}0\\ 2\\ x\end{array}\right]=O$, is

• A. 1
• B. 0
• C. -1
• D. 3

Answer 1

Answer: (C)

Given, $\left[\begin{array}{ccc}1& 2& 1\end{array}\right]\left(\left[\begin{array}{ccc}1& 2& 0\\ 2& 0& 1\\ 1& 0& 2\end{array}\right]\left[\begin{array}{c}0\\ 2\\ x\end{array}\right]\right)=0$
$\to \left[\begin{array}{ccc}1& 2& 1\end{array}\right]\left[\begin{array}{ccc}1& 2& 0\\ 2& 0& 1\\ 1& 0& 2\end{array}\right]\left[\begin{array}{c}0\\ 2\\ x\end{array}\right]=0$
$\to \left[\begin{array}{ccc}1& 2& 1\end{array}\right]\left[\begin{array}{c}0+4+0\\ 0+0+x\\ 0+0+2x\end{array}\right]=0$
( $\because$ matrix multiplication is associative)
$\to \left[\begin{array}{ccc}1& 2& 1\end{array}\right]\left[\begin{array}{c}4\\ x\\ 2x\end{array}\right]=0\to [4+2x+2x]=0$
$\to 4+4x=0\to x=-1$