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 $A^{-1}=\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right],$ find $(AB)^{-1}$.

If $A$ and $B$ are two matrices given by $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}$,then the value of $|\operatorname{Adj}(AB)|$ is

If $A$ and $B$ are invertible matrices,which one of the following statements is not correct?

Find the inverse of the matrix $A = \left[\begin{array}{ll}4 & 5 \\ 3 & 4\end{array}\right]$,if it exists.

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$ and $\operatorname{adj} A=\left[\begin{array}{ccc}4 & -1 & 1 \\ 8 & -7 & a \\ 9 & -6 & b\end{array}\right]$,then find the values of $a$ and $b$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module