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et 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 how that W is not a vector space. 4a + 26 5b + 2c 8c + 8a 7b Felect the correct choice and fill in the answer box as needed to complete your choice.

et 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 how that W is not a vector space. 4a + 26 5b + 2c 8c + 8a 7b Felect the correct choice and fill in the answer box as needed to complete your choice.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. 4a + 2b 5b + 2c 8c + 8a 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.) O B. There is no spanning set of W because W does not contain the zero vector. O 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 S of vectors that spans W or give an example or an explanation to show that W is not a vector space. 4a + 2b 5b + 2c 8c + 8a 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.) O B. There is no spanning set of W because W does not contain the zero vector. O 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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