Question

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Let A be an orthogonal n times n matrix. (1) Prove that for every vectors x vector, y vector elementof R^n, the angle between A x vector and A y vector is the same as the angle between x vector and y vector (in this case, we say that A keeps the angle). (2) Find a matrix B, such that B keeps the angle in the sense of part (a) but B is not orthogonal.

Show transcribed image text Let A be an orthogonal n times n matrix. (1) Prove that for every vectors x vector, y vector elementof R^n, the angle between A x vector and A y vector is the same as the angle between x vector and y vector (in this case, we say that A keeps the angle). (2) Find a matrix B, such that B keeps the angle in the sense of part (a) but B is not orthogonal.