Question: Let L: Rn Rn be a linear operator? (a) Prove that if L is an isometry, then ||L(x)|| = ||x||, for x in R.

Let L: Rn → Rn be a linear operator?
(a) Prove that if L is an isometry, then ||L(x)|| = ||x||, for x in R".
(b) Prove that if L is an isometry and ( is the angle between vectors x and y in Rn, then the angle between L(x) and L(y) is also (?

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