Question

If $P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$ is the ad joint of $3\times 3$ matrix $A$ and $|A|=4$ then $\alpha$ is

• A. 4
• B. 11
• C. 5
• D. 0

Answer 1

Answer: (B)

11

Given, P is adjoint of $3\times 3$ matrix A

$\left|Adj\right(A\left)\right|={\left|A\right|}^{3-1}$

$P={\left|A\right|}^2$

$\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]=4^2$

$1(12-12)-\alpha (4-6)+3(4-6)=16$

$2\alpha -6=16$

$\therefore 2\alpha =22$

$\therefore \alpha =11$