If A = begin{bmatrix} cos theta & sin theta | vedclass

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Question

(A) The transpose of a matrix $A$,denoted by $A'$,is obtained by interchanging its rows and columns. Given $A = \begin{bmatrix} \cos 	heta & \sin 	h

Vedclass · Accepted Answer

$\begin{bmatrix} \cos 	heta & -\sin 	heta \ \sin 	heta & \cos 	heta \end{bmatrix}$

Vedclass · Answer

(A) The transpose of a matrix $A$,denoted by $A'$,is obtained by interchanging its rows and columns. Given $A = \begin{bmatrix} \cos 	heta & \sin 	heta \ -\sin 	heta & \cos 	heta \end{bmatrix}$. To find $A'$,we swap the elements of the first row with the first column and the second row with the second column. Thus,$A' = \begin{bmatrix} \cos 	heta & -\sin 	heta \ \sin 	heta & \cos 	heta \end{bmatrix}$. Comparing this with the given options,option $A$ is the correct answer.

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$,then $A' = $ . . . . . . .

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