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 + 4b 7b + 5c 9c + 4a 5b Select the correct choice and fill in the answer box as needed to complete your choice. A. A spanning set is S = 0. (Use a comma to separate answers as needed.) There is no spanning set of W because W does not contain the zero vector. There is no spanning set of W because W is not closed under scalar multiplication. B. C. D. There is no spanning set of W because W is not closed under vector addition.
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 + 4b 7b + 5c 9c + 4a 5b Select the correct choice and fill in the answer box as needed to complete your choice. A. A spanning set is S = 0. (Use a comma to separate answers as needed.) There is no spanning set of W because W does not contain the zero vector. There is no spanning set of W because W is not closed under scalar multiplication. B. C. D. There is no spanning set of W because W is not closed under vector addition.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
2a + 4b
7b + 5c
9c + 4a
5b
Select the correct choice and fill in the answer box as needed to complete your
choice.
A. A spanning set is S = 0.
(Use a comma to separate answers as needed.)
There is no spanning set of W because W does not contain the zero vector.
There is no spanning set of W because W is not closed under scalar
multiplication.
B.
C.
D. There is no spanning set of W because W is not closed under vector
addition.
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