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Consider the inner product space P1[0, 1] with Find a unit vector that is orthogonal to f(x) = 2x - 1. For any real matrix An times n with eta(A) = 0, introduce M = ATA. Prove that : Rn times Rn rightarrow R, given by is an inner product in Rn.

Show transcribed image text Consider the inner product space P1[0, 1] with Find a unit vector that is orthogonal to f(x) = 2x - 1. For any real matrix An times n with eta(A) = 0, introduce M = ATA. Prove that : Rn times Rn rightarrow R, given by is an inner product in Rn.