If A = begin{bmatrix} 3 & 2 1 & 4 end{bmatri | vedclass

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

Question

(A) We know that for any square matrix $A$ of order $n$,$A(	ext{adj } A) = |A|I$,where $I$ is the identity matrix of order $n$.Given $A = \begin{bmat

Vedclass · Accepted Answer

$\begin{bmatrix} 10 & 0 \ 0 & 10 \end{bmatrix}$

Vedclass · Answer

(A) We know that for any square matrix $A$ of order $n$,$A(	ext{adj } A) = |A|I$,where $I$ is the identity matrix of order $n$.Given $A = \begin{bmatrix} 3 & 2 \ 1 & 4 \end{bmatrix}$.First,calculate the determinant $|A| = (3 	imes 4) - (2 	imes 1) = 12 - 2 = 10$.Since $A$ is a $2 	imes 2$ matrix,$I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.Therefore,$A(	ext{adj } A) = |A|I = 10 \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 10 & 0 \ 0 & 10 \end{bmatrix}$.

If $A = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$,then $A(\text{adj } A) = $

Similar Questions

The third element in the second row of the adjoint of a matrix $A = [a_{ij}]_{3 \times 3}$,where $a_{ij} = 2i + j$,is:

Find $adj$ $A$ for $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$.

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

If $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \dots$

Let $A$ be an invertible square matrix of order $3 \times 3$. Then $|(\text{adj} A) \cdot A|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module