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

Chapter3: Determinants

Section3.3: Properties Of Determinants

Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

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