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Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The vectors = Ալ (2,-3, 4, -5,2), uz = (3, -2, 7, 9, 1), = us (-1, 1, 2, 1, -3), U7 = (1,0,-2,3,-2), and generate W. Find a subset of {u1, u2,. = u2 (-6, 9, 12, 15, -6), u4= (2, -8,2,-2, 6), u6 (0, -3, -18, 9, 12), 46= = us (2,-1, 1, -9, 7) ug} that is a basis for W.

Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The vectors = Ալ (2,-3, 4, -5,2), uz = (3, -2, 7, 9, 1), = us (-1, 1, 2, 1, -3), U7 = (1,0,-2,3,-2), and generate W. Find a subset of {u1, u2,. = u2 (-6, 9, 12, 15, -6), u4= (2, -8,2,-2, 6), u6 (0, -3, -18, 9, 12), 46= = us (2,-1, 1, -9, 7) ug} that is a basis for W.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Section 3.4: Number 8

 

8. Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The vectors u1 (2, 3, 4, -5, 2), = - -5,2), u3 (3,-2, 7, -9, 1), ԱՅ = u5 (-1, 1, 2, 1, -3), = u2 (-6, 9, 12, 15, -6), = - u4 (2, -8,2,-2, 6), U6 = (0, -3, -18, 9, 12), = u7 (1,0, 2, 3,-2), and Ug = (2,-1, 1, -9,7) generate W. Find a subset of {u₁, u2,..., us} that is a basis for W.
Transcribed Image Text:8. Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The vectors u1 (2, 3, 4, -5, 2), = - -5,2), u3 (3,-2, 7, -9, 1), ԱՅ = u5 (-1, 1, 2, 1, -3), = u2 (-6, 9, 12, 15, -6), = - u4 (2, -8,2,-2, 6), U6 = (0, -3, -18, 9, 12), = u7 (1,0, 2, 3,-2), and Ug = (2,-1, 1, -9,7) generate W. Find a subset of {u₁, u2,..., us} that is a basis for W.
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