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Part 1: We've seen that most of the vector spaces can be equipped with inner product...

Part 1: We've seen that most of the vector spaces can be equipped with inner product functions.   

Question 1:  Is there a vector space that can not be an inner product space? Justify your answer.

Part 2: Suppose that u and v are two non-orthogonal vectors in an inner product space V,< , >.

Question 2: Can we modify the inner product < , > to a new inner product so that the two vectors become orthogonal? Justify your answer.

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