a Show that the rotation matrix applied to the vector x (x1, x2)t has the geometric effect of rotating x through the angle without changing its magnitude with respect to the l2 norm b Show that the magnitude of x with respect to the l norm can be changed by a rotation matrix cos sin sin cos

Question: a. Show that the rotation matrix applied to the vector x = (x1, x2)t has the geometric effect of rotating x through the angle

a. Show that the rotation matrix

applied to the vector x = (x1, x2)t has the geometric effect of rotating x through the angle Î¸ without changing its magnitude with respect to the l2 norm.
b. Show that the magnitude of x with respect to the lˆž norm can be changed by a rotation matrix.

cos sin -sin cos

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