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Let W be a subspace of R³ spanned by the two vectors The following two questions are related to the subspace W. 5 -0-0 V= 4 2 u= where 3 -6 (a) Find a basis for the orthogonal complement of W assuming that the inner product in W is the standard Euclidean inner product (dot product). (b) Find a basis for the orthogonal complement of W assuming that the inner product in W is defined by the formula (u, v) = U₁v₁ +2u₂v2 + UzV3, -0--0

Let W be a subspace of R³ spanned by the two vectors The following two questions are related to the subspace W. 5 -0-0 V= 4 2 u= where 3 -6 (a) Find a basis for the orthogonal complement of W assuming that the inner product in W is the standard Euclidean inner product (dot product). (b) Find a basis for the orthogonal complement of W assuming that the inner product in W is defined by the formula (u, v) = U₁v₁ +2u₂v2 + UzV3, -0--0

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
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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Let W be a subspace of R³ spanned by the two vectors The following two questions are related to the subspace W. 5 -0-0 -3 = 4 2 u= where 3 (a) Find a basis for the orthogonal complement of W assuming that the inner product in W is the standard Euclidean inner product (dot product). (b) Find a basis for the orthogonal complement of W assuming that the inner product in W is defined by the formula (u, v) = U₁v₁ +2u₂v₂ + U3V3, -0-0 .
Transcribed Image Text:Let W be a subspace of R³ spanned by the two vectors The following two questions are related to the subspace W. 5 -0-0 -3 = 4 2 u= where 3 (a) Find a basis for the orthogonal complement of W assuming that the inner product in W is the standard Euclidean inner product (dot product). (b) Find a basis for the orthogonal complement of W assuming that the inner product in W is defined by the formula (u, v) = U₁v₁ +2u₂v₂ + U3V3, -0-0 .
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