Explanation Given: The set V and S are as follows, V = ℝ 3 S = { ( 10 , − 6 , 5 , ) , ( 3 , − 3 , 2 ) , ( 0 , 0 , 0 ) , ( 6 , 4 , − 1 ) , ( 7 , 7 , − 2 ) } . Approach: A set of vectors { v 1 , v 2 , … , v k } in a vector space V spans V if every vector in V can be written as a linear combination of v 1 , v 2 , … , v k ; that is, if for every v ∈ V , there exists scalars c 1 , c 2 , … , c k such that v = c v 1 + c v 2 + … + c v k . Calculation: Consider an arbitrary vector ( a , b , c ) ∈ ℝ 3 = V Then, To determine (b) To find Whether the set S = { ( 10 , − 6 , 5 , ) , ( 3 , − 3 , 2 ) , ( 0 , 0 , 0 ) , ( 6 , 4 , − 1 ) , ( 7 , 7 , − 2 ) } of vectors is linearly independent or not.

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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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 unde…

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Chapter 4.11, Problem 27AP

To determine

(a)

To find:

Whether S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} spans V=ℝ3.

To determine

(b)

To find

Whether the set S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} of vectors is linearly independent or not.

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Chapter 4.11, Problem 26AP

Chapter 4.11, Problem 28AP

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Differential Equations and Linear Algebra (4th Edition)

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(a) To find: Whether S = { ( 10 , − 6 , 5 , ) , ( 3 , − 3 , 2 ) , ( 0 , 0 , 0 ) , ( 6 , 4 , − 1 ) , ( 7 , 7 , − 2 ) } spans V = ℝ 3 .

Solution Summary: The author explains that the set of vectors does not span V if every vector can be written as a linear combination of v_1,

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(a)

To find:

Whether S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} spans V=ℝ3.

(b)

To find

Whether the set S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} of vectors is linearly independent or not.

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Chapter 4 Solutions

(a) To find: Whether S = { ( 10 , − 6 , 5 , ) , ( 3 , − 3 , 2 ) , ( 0 , 0 , 0 ) , ( 6 , 4 , − 1 ) , ( 7 , 7 , − 2 ) } spans V = ℝ 3 .

Solution Summary: The author explains that the set of vectors does not span V if every vector can be written as a linear combination of v_1,

Concept explainers

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(a) To find: Whether S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} spans V=ℝ3.

(b) To find Whether the set S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} of vectors is linearly independent or not.

Want to see the full answer?

Chapter 4 Solutions

(a)

To find:

Whether S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} spans V=ℝ3.

(b)

To find

Whether the set S={(10,−6,5,),(3,−3,2),(0,0,0),(6,4,−1),(7,7,−2)} of vectors is linearly independent or not.