Question

If $\left[\begin{array}{ccc}5& x& 1\end{array}\right]\left[\begin{array}{c}2\\ -1\\ 3\end{array}\right]=\left(20\right)$, then the value of $x$ is

• A. $7$
• B. $-7$
• C. $\frac{1}{7}$
• D. $0$

Answer 1

The correct option is B $-7$

Given expression: ${\left[\begin{array}{ccc}5& x& 1\end{array}\right]}_{1\times 3}\times {\left[\begin{array}{c}2\\ -1\\ 3\end{array}\right]}_{3\times 1}={\left(\begin{array}{c}20\end{array}\right)}_{1\times 1}\Rightarrow {(10+(-x)+3)}_{1\times 1}={\left(\begin{array}{c}20\end{array}\right)}_{1\times 1}$

$\Rightarrow 13-x=20$ [by equality of matrix]

$\Rightarrow x=-7$