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. 5a + 9b 8b-3c 2c+4a 2b Select the corect 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 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. 5a + 9b 8b-3c 2c+4a 2b Select the corect 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 scalar multiplication. O 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

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

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.
5a + 9b
8b-3c
2c + 4a
2b
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 scalar multiplication.
O D. There is no spanning set of W because W is not closed under vector addition.

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