First slide

Operations of matrix

Question

If $A_{α} = [\begin{array}{cc} \cos α & \sin α \\ - \sin α & \cos α \end{array}]$ , then $A_{α} A_{β}$ is equal to

Moderate

A

$A_{α + β}$
B

$A_{α β}$
C

$A_{α - β}$
D

none of these

Solution

We have
$A_{α} A_{β} = [\begin{array}{cc} \cos α & \sin α \\ - \sin α & \cos α \end{array}] [\begin{array}{cc} \cos β & \sin β \\ - \sin β & \cos β \end{array}]$
$= [\begin{matrix} \cos α \cos β - \sin α \sin β \\ - \sin α \cos β - \cos α \sin β \end{matrix} \begin{matrix} \cos α \sin β + \sin α \cos β \\ - \sin α \sin β + \cos α \cos β \end{matrix}]$
$= [\begin{array}{cc} \cos (α + β) & \sin (α + β) \\ - \sin (α + β) & \cos (α + β) \end{array}] = A_{α + β}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App