5. Inner Product Spaces••Prove that the space C[a, b] of continuous functions over [a, b] with the inner product(f,g) = f f (x)g(x)dx is an inner product space.Use the Gram-Schmidt process to orthogonalize the vectors (1, 1, 0), (1, 0, 1), and(0, 1, 1).

Step 1: Step 2: Step 3: Step 4:

Answered: 5. Inner Product Spaces • • Prove that…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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No. 6 (a, b, c)
1. Let V = C[-2, 2], the vector space of continuous functions on the closed interval [-2, 2]. Let f, g E V and define the inner product of f and g to be (f, g) = | f(x)g(x) dx. Let h(x) = x? and let k(x) = 7x*, compute (h, k). Simplify your answer completely.

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5. Inner Product Spaces • • Prove that the space C[a, b] of continuous functions over [a, b] with the inner product (f,g) = f f (x)g(x)dx is an inner product space. Use the Gram-Schmidt process to orthogonalize the vectors (1, 1, 0), (1, 0, 1), and (0, 1, 1).