The positive value of the determinant of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We know that for a square matrix $A$ of order $n$,$\operatorname{Adj}(\operatorname{Adj}(A)) = |A|^{n-2} A$. Taking the determinant on both sides,

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(B) We know that for a square matrix $A$ of order $n$,$\operatorname{Adj}(\operatorname{Adj}(A)) = |A|^{n-2} A$. Taking the determinant on both sides,$|\operatorname{Adj}(\operatorname{Adj}(A))| = (|A|^{n-2})^n = |A|^{(n-1)^2}$. Here,the matrix is of order $n=3$,so $|\operatorname{Adj}(\operatorname{Adj}(A))| = |A|^{(3-1)^2} = |A|^4$. Now,calculate the determinant of the given matrix: $|\operatorname{Adj}(\operatorname{Adj}(A))| = \begin{vmatrix} 14 & 28 & -14 \ -14 & 14 & 28 \ 28 & -14 & 14 \end{vmatrix} = 14^3 \begin{vmatrix} 1 & 2 & -1 \ -1 & 1 & 2 \ 2 & -1 & 1 \end{vmatrix}$. $= 14^3 [1(1 - (-2)) - 2(-1 - 4) - 1(1 - 2)] = 14^3 [1(3) - 2(-5) - 1(-1)] = 14^3 [3 + 10 + 1] = 14^3 	imes 14 = 14^4$. Thus,$|A|^4 = 14^4$. Since we need the positive value,$|A| = 14$.

The positive value of the determinant of the matrix $A$,whose $\operatorname{Adj}(\operatorname{Adj}(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}$,is

Similar Questions

If $\begin{bmatrix} 1 & -\tan \theta \\ \tan \theta & 1 \end{bmatrix} \begin{bmatrix} 1 & \tan \theta \\ -\tan \theta & 1 \end{bmatrix}^{-1} = \begin{bmatrix} a & -b \\ b & a \end{bmatrix}$,then

$A$ is an involutory matrix given by $A = \begin{bmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\ 3 & -3 & 4 \end{bmatrix}$. Then the inverse of $\frac{A}{2}$ will be:

If $A = \begin{bmatrix} 2 & 3 \\ 4 & 6 \end{bmatrix}$,then ${A^{-1}} = $

The inverse matrix of $\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix}$ is

If $A$ is a matrix of order $2$ and $I$ is the identity matrix of order $2$ such that $A^2 - 4A + 3I = 0$,then $(A + 3I)^{-1} =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module