Question: Let V denote a vector space together with an inner product < , > : V V R. Let x , y be non-zero vectors

Let V denote a vector space together with an inner product <, > : V V R.

Let x, y be non-zero vectors in V .

(a) Prove or disprove that if x and y are orthogonal, then they are linearly independent.

(b) Prove or disprove that if x and y are linearly independent, then they are orthogonal.

(c) How do the above statements change if we remove the restriction that x and y have to be non-zero?

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