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. 2a + 7b 0 a+b+c c-3a

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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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 S of vectors that spans W or give an
example or an explanation to show that W is not a vector space.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The set W is a vector space and a spanning set is S = {}.
(Use a comma to separate vectors as needed.)
B.
The set W is not a vector space because W does not contain the zero vector.
C. The set W is not a vector space because W is not closed under vector addition.
D. The set W is not a vector space because W is not closed under scalar multiplication.
2a + 7b
0
a+b+c
c-3a
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 S of vectors that spans W or give an example or an explanation to show that W is not a vector space. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The set W is a vector space and a spanning set is S = {}. (Use a comma to separate vectors as needed.) B. The set W is not a vector space because W does not contain the zero vector. C. The set W is not a vector space because W is not closed under vector addition. D. The set W is not a vector space because W is not closed under scalar multiplication. 2a + 7b 0 a+b+c c-3a
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