Question: 1. Let f, g E C[0, 1], where C[0, 1] is the set of all functions that are continuous on the interval 0, 1]. Define

1. Let f, g E C[0, 1], where C[0, 1] is the set of all functions that are continuous on the interval 0, 1]. Define the inner product ( f, g) = ( f(x)g(a) dac for f, g E C[0, 1]. Answer the following. A. Show that ( f, g) is an inner product. B. Find (ac, a2 + 1). 2. Let p, q E P2. Define (p, q) = p(x) q(x) dac. 1. Show that (p, q) is an inner product. 2. Find (ac2 + 1, ac - 1). 3. Find cos of the angle between the two vectors p(a ) = 2x2 - 3x - 1 and q(x) = x - 3. 4. Find | |202 - 3|1. 3. Let ( A, B) = trace(At B). 2 1. Find

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