Question: Suppose that v1=(1,1,1,1), v2=(2,2,2,2), and v3=(3,3,3,3).  Which of the following vectors are in span ? Explain your work. A) (2, 3, -7, 3) B) (0, 0, 0 ,0) C) (1, 1, 1, 1) D) (-4, 6, -13, 4)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...
icon
Related questions
Question

Question:

Suppose that v1=(1,1,1,1), v2=(2,2,2,2), and v3=(3,3,3,3).  Which of the following vectors are in span ? Explain your work.

A) (2, 3, -7, 3)

B) (0, 0, 0 ,0)

C) (1, 1, 1, 1)

D) (-4, 6, -13, 4)

My Comments:

I've attempted this problem by setting the vectors equal to the multiple choice answers. I placed them in augmented form and took the reduced row echelon form. However, so far A and B are coming out equal making me conclude that A and B are in span. Am I solving this correctly? Did I get it right?

Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

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
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
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