If P = \left[ {\begin{matrix} 1 & \alpha & 3 \ 1 & 3 & 3 \ 2 & 4 & 4 \ \end{matrix} } ight] is the adjoint of a 3 imes 3 matrix A and \left| A ight| = 4, then \alpha is equal to :

Question

If P = \left[ {\begin{matrix} 1 & \alpha & 3 \ 1 & 3 & 3 \ 2 & 4 & 4 \ \end{matrix} } ight] is the adjoint of a 3 	imes 3 matrix A and \left| A ight| = 4, then \alpha is equal to :

Accepted Answer

Answer: B. 11 \left| P \right| = 1\left( {12 - 12} \right) - \alpha \left( {4 - 6} \right) + \,\,\,\,\,\,\,\,\,\,\,3\left( {4 - 6} \right) = 2\alpha - 6 Now, adj\,\,A = P\, \,\,\,\,\,\,\,\, \Rightarrow \left| {adj\,A} \right| = \left| P \right| \Rightarrow {\left| A \right|^2} = \left| P \right| \Rightarrow \left| P \right| = 16 \Rightarrow 2\alpha - 6 = 16 \Rightarrow \alpha = 11

If $$P = \left[ {\begin{matrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \\ \end{matrix} } \right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and $$\left| A \right| = 4,$$ then $$\alpha $$ is equal to :

Answer

Explanation

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