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 spansW or give an example or an explanation to show that W is not a vector space.За + 6b5b – 6c9с - ба2bSelect 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 vector addition. Show that w is in the subspace of R spanned by v,, v2, and va, where these vectors are defined as follows.-7-66-7V19- 5w =V, =V3 =- 3- 2- 5161115To show that w is in the subspace, express w as a linear combination of v,, v2, and v3. Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice.O A. The vector w is in the subspace spanned by v1, v2, and v3. It is given by the formula w=Ov, + Dv2 + (_ 3-(Simplify your answers. Type integers or fractions.)O B. The vector w is not in the subspace spanned by v,, v2, and v3-

Hey, since there are multiple questions posted, we will answer first question. If you want any specific question to be answered then please submit that question only or specify the question number in your message It is given that W be set o all vectors of form 3a+6b5b-6c9c-6a2b. Factor out scalars as: Let u=30-90,v=6502,w=0-690. Equate 3a+6b5b-6c9c-6a2b=a30-90+b6502+c0-690 to 0: a30-90+b6502+c0-690=03a+6b=05b-6c=0-9a+9c=02b=0Substitute b=0 in 3a+6b=0 and 5b-6c=0: 3a+60=0a=050-6c=0c=0 Hence, the zero vectors are in W. Thus, the set of vectors spans W . A spanning set is S=30-90,6502,0-690.

Math

Advanced Math

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. За + 6b 5b - 6c 9с - ба 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 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. За + 6b 5b - 6c 9с - ба 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 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.
За + 6b
5b – 6c
9с - ба
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.
OC. There is no spanning set of W because W is not closed under vector addition.

Show that w is in the subspace of R spanned by v,, v2, and va, where these vectors are defined as follows.
-7
-6
6-
7
V1
9
- 5
w =
V, =
V3 =
- 3
- 2
- 5
16
11
15
To show that w is in the subspace, express w as a linear combination of v,, v2, and v3. Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice.
O A. The vector w is in the subspace spanned by v1, v2, and v3. It is given by the formula w=
Ov, + Dv2 + (_ 3-
(Simplify your answers. Type integers or fractions.)
O B. The vector w is not in the subspace spanned by v,, v2, and v3-

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