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Vith respect to the above inner product, select all the orthonormal bases of R³. (1, 0, 0)¹, (0, 1, 0), (0, 0, 1)¹ (1,0,0), (0,0), (0,0₁%) T T T (1,0,1),(₁,0,1),(0,2,0) T (0) (-1,0), (0,0,)*

Vith respect to the above inner product, select all the orthonormal bases of R³. (1, 0, 0)¹, (0, 1, 0), (0, 0, 1)¹ (1,0,0), (0,0), (0,0₁%) T T T (1,0,1),(₁,0,1),(0,2,0) T (0) (-1,0), (0,0,)*

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)² € R³. 3 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, 0), (0,0₁) 9 T ¡‚ 0, ¹) ª, (1, 0, −1¹)¹, (0, √2, T T 0) ² T T T (↓⁄2‚½‚0)˜‚ (½‚ −1,0)², (0,0, ½)″ 1 2'
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)² € R³. 3 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, 0), (0,0₁) 9 T ¡‚ 0, ¹) ª, (1, 0, −1¹)¹, (0, √2, T T 0) ² T T T (↓⁄2‚½‚0)˜‚ (½‚ −1,0)², (0,0, ½)″ 1 2'
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