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I am having trouble with these questions-

Explain/prove whether:

(a) Any set {v1,v2,.....vk} of orthogonal vectors in Rn is linearly independent.

(b) If there is a vector v in Rn and scalar c in R, we have ||cv|| = c||v||

(c) for any vectors u, v in Rn, ||u+v||^2 + ||u-v||^2 = 2 ||u||^2 + 2||v||^2

I think part a is true, but can't get around a way to prove it. Need help with b and c.

Explain/prove whether:

(a) Any set {v1,v2,.....vk} of orthogonal vectors in Rn is linearly independent.

(b) If there is a vector v in Rn and scalar c in R, we have ||cv|| = c||v||

(c) for any vectors u, v in Rn, ||u+v||^2 + ||u-v||^2 = 2 ||u||^2 + 2||v||^2

I think part a is true, but can't get around a way to prove it. Need help with b and c.

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