5. Let V be a vector space over R, and suppose that v1, v2, v3, V4 are linearly independent vectors in V. a. Prove that the vectors Vị – V3, 2v2 – 3v3 + V4, -vi + 4v2 + 2v3 + v4, vị + 2v2 + 3v3 are linearly dependent. b. Prove that the vectors vị + v2 + V3 + v4, Vi – V2, vi + v2 – 2v3 + v4, 3v3 – V4 are linearly independent.
5. Let V be a vector space over R, and suppose that v1, v2, v3, V4 are linearly independent vectors in V. a. Prove that the vectors Vị – V3, 2v2 – 3v3 + V4, -vi + 4v2 + 2v3 + v4, vị + 2v2 + 3v3 are linearly dependent. b. Prove that the vectors vị + v2 + V3 + v4, Vi – V2, vi + v2 – 2v3 + v4, 3v3 – V4 are linearly independent.
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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