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Consider the inner product space R³ with (,) = U₁v₁ + 2u₂v₂ + 3u3v3 for every = (u₁, U2, U3) 12, U3)², V = (V₁, V2, V3)⁰ € R³. With respect to the above inner product, select all the orthonormal bases of R³ . 0000 (1,0,0), (0, 1,0), (0, 0, 1) T (1,0,0), (0, ,0), (0.0,) T (¹,0,1),(1,0,¹),(0, -2,0) ² (1.0), (1.0), (0.0,-) T

Consider the inner product space R³ with (,) = U₁v₁ + 2u₂v₂ + 3u3v3 for every = (u₁, U2, U3) 12, U3)², V = (V₁, V2, V3)⁰ € R³. With respect to the above inner product, select all the orthonormal bases of R³ . 0000 (1,0,0), (0, 1,0), (0, 0, 1) T (1,0,0), (0, ,0), (0.0,) T (¹,0,1),(1,0,¹),(0, -2,0) ² (1.0), (1.0), (0.0,-) T

Elementary Linear Algebra (MindTap Course List)
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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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
Transcribed Image Text: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
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