Question

Consider the canonical basis (e1, e2) of the two-dimensional Cartesian space

Consider the canonical basis (e1, e2) of the two-dimensional Cartesian space. Rotate the basis by an angle a counterclockwise. Show that the original cartesian variables (x1, x2) are related to the rotated variables (y1, y2) according to x = Ay, or equivalently,

Show that A is orthogonal.

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