If P = \left[\right. 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \left]\right. is the adjoint of a 3 × 3 matrix A and | A

Engineering

Mathematics

Transpose and Adjoint of a Matrix

Question

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

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

| adj A | = | A |² = 4² = 16

$| \begin{matrix} 1 & α & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{matrix} |$ = 16

$\Rightarrow$ 2 $α$ – 6 = 16

$\Rightarrow α$ = 11.