Question

If $\begin{bmatrix}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{bmatrix}\begin{bmatrix}- x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x \end{bmatrix}=\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$ then find the value of $x$

• A. $\frac{1}{2}$
• B. $\frac{1}{5}$
• C. No unique value of 'x'
• D. None of these

Answer 1

Answer: (B)

We have $\begin{bmatrix}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{bmatrix}$
$\begin{bmatrix}- x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x \end{bmatrix} =\begin{bmatrix}5x & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 10x-2 & 5x\end{bmatrix}$
$=\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$
$\Rightarrow x = 1/5$