Explanation Given: The vector space V is M 2 ( ℝ ) . And the vector space S is { [ 1 2 2 1 ] , [ 3 4 4 3 ] , [ − 2 − 1 − 1 − 2 ] , [ − 3 0 0 3 ] , [ 2 0 0 0 ] } . Approach: If the system of equation has greater number of unknown than the number of equations, then the system is inconsistent. Calculation: Consider an arbitrary vector A = [ a b c d ] Suppose, A 1 = [ 1 2 2 1 ] , A 2 = [ 3 4 4 3 ] , A 3 = [ − 2 − 1 − 1 − 2 ] Then, A = c 1 A 1 + c 2 A 2 + c 3 A 3 + c 4 A 4 + c 5 A 5 Substitute [ 1 2 2 1 ] for A 1 , [ 3 4 4 3 ] for A 2 , [ − 2 − 1 − 1 − 2 ] for A 3 and [ a b c d ] for A in above equation To determine (b) To find Whether S of vectors is linearly independent or not.

Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

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ISBN: 9780321985811

Author: Stephen W. Goode, Scott A. Annin

Publisher: Pearson (edition 4)

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Chapter 4.11, Problem 31AP

To determine

(a)

To find:

Whether S of vectors has span V or not.

To determine

(b)

To find

Whether S of vectors is linearly independent or not.

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Chapter 4.11, Problem 30AP

Chapter 4.11, Problem 32AP

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Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

Ch. 4.1 - True-False Review For items a-I, decide if the...Ch. 4.1 - Prob. 2TFR Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - Prob. 7TFR Ch. 4.1 - Prob. 8TFR Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - Prob. 10TFR

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(a) To find: Whether S of vectors has span V or not.

Solution Summary: The author explains that the set S of vectors does not span V.