Question

If $A=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$ is a $3\times 3$ matrix and $|A|=4$ then $\alpha$ is-

• A. $4$
• B. $11$
• C. $5$
• D. $0$

Answer 1

Answer: (C)

$5$

$|A|=4$ [ Given ]

$|A|=\left|\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right|$

$\Rightarrow$ $4=1(12-12)-\alpha (4-6)+3(4-6)$

$\Rightarrow$ $4=0+2\alpha -6$

$\Rightarrow$ $4+6=2\alpha$

$\Rightarrow$ $2\alpha =10$

$\Rightarrow$ $\alpha =\frac{10}{2}$

$\therefore$ $\alpha =5$