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Define the following on R3: 〈(a, b, c), (a′, b′, c′)〉 = 2aa′ + bb′ +...

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Advance Math

Define the following on R3:
〈(a, b, c), (a′, b′, c′)〉 = 2aa′ + bb′ + 3cc′.

(a) Prove that 〈 , 〉 is an inner product on R3.
(b) Let B = {(1,1,0),(1,0,1),(0,1,1)}. Is B an orthogonal basis forR3 under the inner product defined above. If not, use theGram-Schmidt algorithm to transform B into an orthogonal basis.

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