The positive value of the determinant of the matrix A, whose A d … - Vidyadip

MCQ

The positive value of the determinant of the matrix $A$, whose $A d j(A d j(A))=\left(\begin{array}{ccc}14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right)$, is

A
$13$
✓
$14$
C
$15$
D
$16$

✓

Answer

Correct option: B.

$14$

b
$\operatorname{Adj}(\operatorname{Adj} A)=\left[\begin{array}{ccc}14 & 18 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right]$

$|\operatorname{Adj}(\operatorname{Adj} A)|=\left[\begin{array}{ccc}14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right]=14 \times 14 \times 14\left|\begin{array}{ccc}1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1\end{array}\right|$

$=(14)^{3}[3-2(-5)-1(-1)]=(14)^{3}[14]=(14)^{4}$

$|A|^{4}=(14)^{4} \Rightarrow|A|=14$

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