Let W denote the subspace of R5 consisting of all vectors having coordinates that sum to zero. The vectors u1= (2,−3, 4,−5, 2), u2 = (−6, 9,−12, 15,−6),u3 = (3,−2, 7,−9, 1), u4 = (2,−8, 2,−2, 6),u5= (−1, 1, 2, 1,−3), u6 = (0,−3,-18, 9, 12),u7 = (1, 0,−2, 3,−2),and u8 = (2,−1, 1,−9, 7)generate W. Find a subset of {u1, u2, . . . ,u8} that is a basis for W.
Let W denote the subspace of R5 consisting of all vectors having coordinates that sum to zero. The vectors u1= (2,−3, 4,−5, 2), u2 = (−6, 9,−12, 15,−6),u3 = (3,−2, 7,−9, 1), u4 = (2,−8, 2,−2, 6),u5= (−1, 1, 2, 1,−3), u6 = (0,−3,-18, 9, 12),u7 = (1, 0,−2, 3,−2),and u8 = (2,−1, 1,−9, 7)generate W. Find a subset of {u1, u2, . . . ,u8} that is a basis for W.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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Let W denote the subspace of R5 consisting of all
The vectors u1= (2,−3, 4,−5, 2), u2 = (−6, 9,−12, 15,−6),u3 = (3,−2, 7,−9, 1), u4 = (2,−8, 2,−2, 6),u5= (−1, 1, 2, 1,−3), u6 = (0,−3,-18, 9, 12),u7 = (1, 0,−2, 3,−2),and u8 = (2,−1, 1,−9, 7)generate W.
Find a subset of {u1, u2, . . . ,u8} that is a basis for W.
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