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Question 2.1.16: ( a) What 2 by 2 matrix R rotates every vector by 90°? R tim...

( a) What 2 by 2 matrix R rotates every vector by 90°? R times [xy]\left[ \begin{matrix} x \\ y \end{matrix} \right] is [y−x]\left[ \begin{matrix} y \\ -x \end{matrix} \right].
(b) What 2 by 2 matrix R2{R}^{2} rotates every vector by 180°?

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( a) 90° rotation from 

R=[01−10]R=\left[ \begin{matrix} 0 & 1 \\ -1 & 0 \end{matrix} \right] ,

( b) 180° rotation from

R2=[−100−1]=−I{R}^{2}=\left[ \begin{matrix} -1 & 0 \\ 0 & -1 \end{matrix} \right] =-I.

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