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 + 6b 7b - 8c 4c + 2a 8b 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. OC. There is no spanning set of W because W is not closed under scalar multiplication. O 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. 4a + 6b 7b - 8c 4c + 2a 8b 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. OC. There is no spanning set of W because W is not closed under scalar multiplication. O D. There is no spanning set of W because W is not closed under vector addition.

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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