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Part A) Consider the inner product space (R³, (.,.)), where (u, v) = u Av, Vu, ʊ € R³, and Let and define the set 1 2 1 A = 2 5 1 1 2 3 1 I = 1 0 (}) S = {R³ | is orthogonal to }, which can be shown to be a subspace of R3. Find a basis for S. Part B) Resolve using matrix below as new "A" For problem above. Explain why new matrix A is correct and original A matrix is incorrect. 1 2 1 A = = 2 52 . 1 2 3

Part A) Consider the inner product space (R³, (.,.)), where (u, v) = u Av, Vu, ʊ € R³, and Let and define the set 1 2 1 A = 2 5 1 1 2 3 1 I = 1 0 (}) S = {R³ | is orthogonal to }, which can be shown to be a subspace of R3. Find a basis for S. Part B) Resolve using matrix below as new "A" For problem above. Explain why new matrix A is correct and original A matrix is incorrect. 1 2 1 A = = 2 52 . 1 2 3

Elementary Linear Algebra (MindTap Course List)
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 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
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Part A) Consider the inner product space (R³, (.,.)), where (u, v) = u Av, Vu, ʊ € R³, and Let and define the set 1 2 1 A = 2 5 1 1 2 3 1 I = 1 0 (}) S = {R³ | is orthogonal to }, which can be shown to be a subspace of R3. Find a basis for S. Part B) Resolve using matrix below as new "A" For problem above. Explain why new matrix A is correct and original A matrix is incorrect. 1 2 1 A = = 2 52 . 1 2 3
Transcribed Image Text:Part A) Consider the inner product space (R³, (.,.)), where (u, v) = u Av, Vu, ʊ € R³, and Let and define the set 1 2 1 A = 2 5 1 1 2 3 1 I = 1 0 (}) S = {R³ | is orthogonal to }, which can be shown to be a subspace of R3. Find a basis for S. Part B) Resolve using matrix below as new "A" For problem above. Explain why new matrix A is correct and original A matrix is incorrect. 1 2 1 A = = 2 52 . 1 2 3
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