Is the following questions below a NEVER TRUE, SOMETIMES TRUE, or ALWAYS TRUE. a.) The set of all linear combinations of v1,...,vn is a vector space. b.) For m = n-1, if {v_1,...,v_m} spans V then S spans V. c.) For m = n-1, if {v_1,...,v_m} is linearly independent then so is S. d.) If dim V = n and span S = V then S can be linearly dependent.

Is the following questions below a NEVER TRUE, SOMETIMES TRUE, or ALWAYS TRUE. a.) The set of all linear combinations of v1,...,vn is a vector space. b.) For m = n-1, if {v_1,...,v_m} spans V then S spans V. c.) For m = n-1, if {v_1,...,v_m} is linearly independent then so is S. d.) If dim V = n and span S = V then S can be linearly dependent.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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