Discussion Forum

If P=  $\begin{bmatrix}1 & \alpha &3 \\1 & 3&3 \\2&4& 4 \end{bmatrix}$   is the adjoint of a 3x 3  matrix A and |A| =4,  then $\alpha$ is equal  to

Answer:

Explanation:

Given , P=  $\begin{bmatrix}1 & \alpha &3 \\1 & 3&3 \\2&4& 4 \end{bmatrix}$ 

  $\therefore$     |P| = 1(12-12)- $\alpha$ (4-6) +3(4-6)

  = 2$\alpha$-6

$\because$  P=adj(A)           (given)

$\therefore$            |P|=|adj A|=|A|², =16

                                   ($\because$   |adj  A|=|A|^n-1)

 $\therefore$       2$\alpha$-6=16

   $\Rightarrow$      $2\alpha=22\Rightarrow\alpha=11$