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Use the Cauchy-Schwarz inequality in an inner product space to show that:
(a) If | u || < 1, then (u,v)2 < ||v||2 for all v in V.
(b) (x cosθ + y sinθ) y2 < x2 + y2 for all real x,y, and θ.
(c) ||r1v1 + - + rnvn||2 < [r1 ||+ - + rn|| v||]2 for all vectors v" and all r, > 0 in R. |
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