cos theta begin{bmatrix} cos theta & sin thet | vedclass

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

Question

(D) Multiply the scalar $\cos 	heta$ into the first matrix and $\sin 	heta$ into the second matrix:$\begin{bmatrix} \cos^2 	heta & \cos 	heta \sin

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Multiply the scalar $\cos 	heta$ into the first matrix and $\sin 	heta$ into the second matrix:$\begin{bmatrix} \cos^2 	heta & \cos 	heta \sin 	heta \ - \sin 	heta \cos 	heta & \cos^2 	heta \end{bmatrix} + \begin{bmatrix} \sin^2 	heta & - \sin 	heta \cos 	heta \ \sin 	heta \cos 	heta & \sin^2 	heta \end{bmatrix}$Now,add the corresponding elements of the two matrices:$= \begin{bmatrix} \cos^2 	heta + \sin^2 	heta & \cos 	heta \sin 	heta - \sin 	heta \cos 	heta \ - \sin 	heta \cos 	heta + \cos 	heta \sin 	heta & \cos^2 	heta + \sin^2 	heta \end{bmatrix}$Using the trigonometric identity $\cos^2 	heta + \sin^2 	heta = 1$,we get:$= \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$

$\cos \theta \begin{bmatrix} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} + \sin \theta \begin{bmatrix} \sin \theta & - \cos \theta \\ \cos \theta & \sin \theta \end{bmatrix} = $

Similar Questions

If $A$ and $B$ are two matrices and $(A + B)(A - B) = A^2 - B^2$,then

If $A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then the incorrect option among the following is

In an upper triangular matrix of order $n \times n$,the minimum number of zeros is:

If $A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$,then ${A^n} = $

For matrix $A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$, if $A^2 - 2I = KA$, then $K = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module