\text { Let } V=\mathbf{R}^{2}, \text { and let } \mathcal{C} \text { be the natural basis for } \mathbf{R}^{2} Consider the linear operator R/6 : V → V where R/6(v) is the vector v rotated /6radians anti-clockwise around the origin. Show (using a carefully-drawn diagram) that \left[R_{\pi / 6}\right] c=\left(\begin{array}{cc} \sqrt{3} / 2 & -1 / 2 \\ 1 / 2 & \sqrt{3} / 2 \end{array}\right) Prove, moreover, that R/6 is a linear isomorphism. ) Consider the linear operator s-2x : V →V where s-2x (v) is the vector v reflected in the line y = -2x. Calculate [s-22]c and verify that this matrix squares to give the identity.S.

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