If \(P=\begin{bmatrix}1&\alpha&3\\1&3&3\\2&4&4\end{bmatrix}\) is the adjoint of a \(3\times3\) matrix \(A\) and \(|A|=4\), then \(\alpha\) is equal to :
Show Hint
- \(4\)
- \(11\)
- \(5\)
- \(0\)
The Correct Option is B
Solution and Explanation
So \(|P|=16\).
Expand along the first row: \(|P|=1(3\cdot4-3\cdot4)-\alpha(1\cdot4-3\cdot2)+3(1\cdot4-3\cdot2)\).
\(=0-\alpha(-2)+3(-2)=2\alpha-6\).
\(2\alpha-6=16\Rightarrow \alpha=11\).
Answer: (2) 11
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