Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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)
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...
See similar textbooks
icon
Related questions
Question
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.
Transcribed Image Text: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.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS