Guided Proof Let u, v be the Euclidean innerproduct on Rn.
Chapter 5, Problem 5.2.95(choose chapter or problem)
Guided Proof Let u, v be the Euclidean innerproduct on Rn. Use the fact that u, v = uTv to provethat for any n n matrix A, (a) ATAu, v = u, Avand(b) ATAu, u = )Au)2.Getting Started: To prove (a) and (b), make use of boththe properties of transposes (Theorem 2.6) and theproperties of the dot product (Theorem 5.3).(i) To prove part (a), make repeated use of the propertyu, v = uTv and Property 4 of Theorem 2.6.(ii) To prove part (b), make use of the propertyu, v = uTv, Property 4 of Theorem 2.6, andProperty 4 of Theorem 5.3.
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