First slide

Operations of matrix

Question

If $A_{α} = [\begin{array}{l} \cos α \sin α \\ - \sin α \cos α \end{array}]$ then that $A_{α} . A_{β} =$

Moderate

A

$A_{α - β}$
B

$A_{β - α}$
C

$A_{α + β}$
D

$A_{β}$

Solution

we have, $A_{α} . A_{β} = [\begin{array}{l} \cos α \sin α \\ - \sin α \cos α \end{array}] [\begin{array}{l} \cos β \sin β \\ - \sin β \cos β \end{array}]$
$= [\begin{array}{l} \cos α \cos β - \sin α \sin β \sin α \cos β + \cos α \sin β \\ - \sin α \cos β - \cos α \sin β \cos α \cos β - \sin α \sin β \end{array}]$
$= [\begin{array}{l} \cos (α + β) \sin (α + β) \\ - \sin (α + β) \cos (α + β) \end{array}]$ $= A_{α + β}$

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