Let V = R³. a) Give a definition of addition + on V that makes (V,+) unable to satisfy property Axiom 2 in the definition of vector space. b) Give a definition of addition '+' on V that makes (V,+) unable to satisfy property Axiom 4 in the definition of vector space. c) Give a definition of scalar multiplication on V that makes (V.) unable to satisfy property Axiom 10 in the definition of vector space.

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Q: 4. For vectors v and ū in an inner product space V, prove that u´ projzu and i are orthogonal.

A: v

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Q: 3) Let V = {("), a,b ER'} (note R* = {r € R|r > 0} ). Define "addition" on V by C) + C) - G)…

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Q: can you show part b) closed under scalar multiplication with matrices?

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Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (x, , y.) +…

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