Consider the inner product space R³ with (u, v) = U₁V₁ +2u2v₂ + 3u3V3 for every π = (U₁, U2, U3)¹, V = (V₁, V2, V3)¹ € R³. With respect to the above inner product, select all the orthonormal bases of R³. (1,0,0), (0, 1,0), (0, 0, 1) T (1,0,0), (0,2,0), (0,0,1) T T T (¹, 0, 1) ¹, (¹, 0, ¹)¹, (0, -2,0) T T (10), (1.0), (0,0₁) T

Consider the inner product space R³ with (u, v) = U₁V₁ +2u2v₂ + 3u3V3 for every π = (U₁, U2, U3)¹, V = (V₁, V2, V3)¹ € R³. With respect to the above inner product, select all the orthonormal bases of R³. (1,0,0), (0, 1,0), (0, 0, 1) T (1,0,0), (0,2,0), (0,0,1) T T T (¹, 0, 1) ¹, (¹, 0, ¹)¹, (0, -2,0) T T (10), (1.0), (0,0₁) T

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 41E: Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform...

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