Let W be the subspace of R5 orthogonal to u1=(1, 3, -2, 1, 1) and u2=(0, 1, 1, -1, 0), u3=(0, 0, -2, 1, 2), that is, W=S⊥, where S={ u1=( 1, 3, -2, 1, 1), u2=(0, 1, 1, -1, 0), u3=(0, 0, -2, 1, 2)}. Find Subtask (1): a basis and the dimension of the subspace W. Subtask (2): an orthogonal basis of the subspace W.
Let W be the subspace of R5 orthogonal to u1=(1, 3, -2, 1, 1) and u2=(0, 1, 1, -1, 0), u3=(0, 0, -2, 1, 2), that is, W=S⊥, where S={ u1=( 1, 3, -2, 1, 1), u2=(0, 1, 1, -1, 0), u3=(0, 0, -2, 1, 2)}. Find Subtask (1): a basis and the dimension of the subspace W. Subtask (2): an orthogonal basis of the subspace W.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...
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Let W be the subspace of R5 orthogonal to u1=(1, 3, -2, 1, 1) and u2=(0, 1, 1, -1, 0), u3=(0, 0, -2, 1, 2), that is, W=S⊥, where S={ u1=( 1, 3, -2, 1, 1), u2=(0, 1, 1, -1, 0), u3=(0, 0, -2, 1, 2)}. Find
Subtask (1): a basis and the dimension of the subspace W.
Subtask (2): an orthogonal basis of the subspace W.
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