(a) A set S1 consists of two vectors of the form u = (u1, u2, u3). Explain why S1 is not a basis for R3. (b) A set S2 consists of four vectors of the form u = (u1, u2, u3). Explain why S2 is not a basis for R3. (c) A set S3 consists of three vectors of the form u = (u1, u2, u3). Determine the conditions under which S3 is a basis for R3.
(a) A set S1 consists of two vectors of the form u = (u1, u2, u3). Explain why S1 is not a basis for R3. (b) A set S2 consists of four vectors of the form u = (u1, u2, u3). Explain why S2 is not a basis for R3. (c) A set S3 consists of three vectors of the form u = (u1, u2, u3). Determine the conditions under which S3 is a basis for R3.
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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(a) A set S1 consists of two
(b) A set S2 consists of four vectors of the form u = (u1, u2, u3). Explain why S2 is not a basis for R3.
(c) A set S3 consists of three vectors of the form u = (u1, u2, u3). Determine the conditions under which S3 is a basis for R3.
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