Question
If $f(\alpha)=A=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]$, find
if(-α) + f(α)
if(-α) + f(α)
✓
Answer
$\begin{aligned} & \mathrm{f}(-\alpha)+\mathrm{f}(\alpha) \\ & =\left[\begin{array}{ccc}\cos \alpha & \sin \alpha & 0 \\ -\sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]+\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]\end{aligned}$
$\begin{aligned} & =\left[\begin{array}{ccc}\cos \alpha+\cos \alpha & \sin \alpha-\sin \alpha & 0+0 \\ -\sin \alpha+\sin \alpha & \cos \alpha+\cos \alpha & 0+0 \\ 0+0 & 0+0 & 1+1\end{array}\right] \\ & =\left[\begin{array}{ccc}2 \cos \alpha & 0 & 0 \\ 0 & 2 \cos \alpha & 0 \\ 0 & 0 & 2\end{array}\right]\end{aligned}$
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