Discussion Forum

1)

If matrix         $A=\begin{bmatrix}3 & -2 & 4 \\1 & 2 & -1\\0 & 1 & 1 \end{bmatrix}$       and

$A^{-1}=\frac{1}{k}adj\left(A\right)$,   then k is

   

Answer:

Option C

Explanation:

If  $A=\begin{bmatrix}3 & -2 & 4 \\1 & 2 & -1\\0 & 1 & 1 \end{bmatrix}$

and $A^{-1}=\frac{1}{k}adj\left(A\right)$                ...(i)

Also, we know  $A^{-1}=\frac{adj\left(A\right)}{\begin{vmatrix}A\\\end{vmatrix}}$              ........(ii)

∴ By comparing (i) and (ii)

${\begin{vmatrix}A\\\end{vmatrix}=k}$

$\Rightarrow{\begin{vmatrix}A\\\end{vmatrix}=\begin{bmatrix}3 & -2 & 4 \\1 & 2 & -1\\0 & 1 & 1 \end{bmatrix}}$

=3(2+1)+2(1+0)+4(1-0)

=9+2+4=15