1. Prove the Cauchy-Schwarz inequality: If u and vare in Rº, then lu - v ≤ ||u||||v|| (1). Also, provide an intuitive re

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1. Prove the Cauchy-Schwarz inequality: If u and vare in Rº, then lu - v ≤ ||u||||v|| (1). Also, provide an intuitive reason as to why this is true.... Hint: divide both sides by ||ul| and think about projections. Also, what is the condition for equality in equation (1)?
2. #2 pg 431 in book (section 10.2) Verify that the set {x + 1,-9x + 5, 6x2 - 6x + 1} is an orthogonal set with respect to the inner product: (p, q) = p(x)q(x) dx and then make the set orthonormal.