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

Which of the following is true for the matrix product $AB$?

Let $A = \begin{bmatrix} -1 & 1 & -1 \\ 1 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ satisfy $A^2 + \alpha(adj(adj(A))) + \beta(adj(A)(adj(adj(A)))) = \begin{bmatrix} 2 & -2 & 2 \\ -2 & 0 & -1 \\ 0 & 0 & -1 \end{bmatrix}$ for some $\alpha, \beta \in R$. Then $(\alpha - \beta)^2$ is equal to . . . . . . .

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $X$ is a $2 \times 2$ matrix such that $AX = I$,then $X =$

If matrices $X$ and $Y$ are inverses of each other,then which of the following is true?

$\begin{aligned} & A(\alpha, \beta)=\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & e^\beta\end{array}\right] \\ & \Rightarrow[A(\alpha, \beta)]^{-1}=\end{aligned}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module