Problem 14 (Orthogonal Matrices). Prove each of the following. 1. P is orthogonal PT is orthogonal. 2. If P is orthogonal, then P-1 is orthogonal. 3. If P, Q are orthogonal, then PQ is orthogonal. Problem 15 (Orthogonal Complement). Consider P2 with the inner product, (f,g) = f(x)g(x)dx. Put W = span(2x+1). Find a basis of W. (1)

Problem 14 (Orthogonal Matrices). Prove each of the following. 1. P is orthogonal PT is orthogonal. 2. If P is orthogonal, then P-1 is orthogonal. 3. If P, Q are orthogonal, then PQ is orthogonal. Problem 15 (Orthogonal Complement). Consider P2 with the inner product, (f,g) = f(x)g(x)dx. Put W = span(2x+1). Find a basis of W. (1)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 69E: Find a basis for R2 that includes the vector (2,2).

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