Let W be the set of all vectors of the form shown on the right, where a, b, and c represent arbitrary real numbers. Find a set S of vectors that spans W or give an example or an explanation to show that W is not a vector space. ба- 9b 9b + 4c 9c-9a 7b

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Let W be the set of all vectors of the form shown on the right, where a, b, and c represent arbitrary real numbers. Find a set of
vectors that spans W or give an example or an explanation to show that W is not a vector space.
ба- 9b
9b + 4c
9c - 9a
7b
--.
Select the correct choice and fill in the answer box as needed to complete your choice.
O A. A spanning set is S= {
(Use a comma to separate answers as needed.)
B. There is no spanning set of W because W does not contain the zero vector.
C. There is no spanning set of W because W is not closed under vector addition.
O D. There is no spanning set of W because W is not closed under scalar multiplication.
Transcribed Image Text:Let W be the set of all vectors of the form shown on the right, where a, b, and c represent arbitrary real numbers. Find a set of vectors that spans W or give an example or an explanation to show that W is not a vector space. ба- 9b 9b + 4c 9c - 9a 7b --. Select the correct choice and fill in the answer box as needed to complete your choice. O A. A spanning set is S= { (Use a comma to separate answers as needed.) B. There is no spanning set of W because W does not contain the zero vector. C. There is no spanning set of W because W is not closed under vector addition. O D. There is no spanning set of W because W is not closed under scalar multiplication.
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