If A = begin{bmatrix} cos x & sin x -sin x & | 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 $A$,the product of the matrix and its adjoint is given by the property: $A \cdot (adj(A)) = |A| \cdot I$,where

Vedclass · Accepted Answer

$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

Vedclass · Answer

(A) We know that for any square matrix $A$,the product of the matrix and its adjoint is given by the property: $A \cdot (adj(A)) = |A| \cdot I$,where $I$ is the identity matrix of the same order.First,we calculate the determinant of matrix $A$:$|A| = \begin{vmatrix} \cos x & \sin x \ -\sin x & \cos x \end{vmatrix} = (\cos x)(\cos x) - (\sin x)(-\sin x) = \cos^2 x + \sin^2 x = 1$.Since $|A| = 1$ and $I = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$,we have:$A \cdot (adj(A)) = 1 \cdot \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$.

If $A = \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix}$,then $A \cdot (adj(A)) = $

Similar Questions

If $A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,then $\left(B^{-1} A^{-1}\right)^{-1}=$

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$,then $\text{adj}(3A^2 + 12A) = \dots$

Matrix $A = \begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix}$. If $xyz = 60$ and $8x + 4y + 3z = 20$,then $A (adj A)$ is equal to:

$A$ 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:

The multiplicative inverse of matrix $\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module