Explanation Given: The subset of matrices of dimension 3 × 4 is S = { A in V : each a i j is an integer } . Approach: To set is said to be a subspace if it satisfies all the following properties for u, v and w in the vector V and the scalars a and b, c1. u + v is a vector in V. c2. a v is a vector in V. a1. u + v = v + u a2. u + ( v + w ) = ( u + v ) + w a3. Existence of identity θ in V such that v + θ = v for all vectors in V. a4. Existence of Inverse − v in V such that v + ( − v ) = θ . m1. a ( b v ) = ( a b ) v m2. a ( u + v ) = a u + a v m3. ( a + b ) v = a v + b v m4. 1 v = v To check whether the subset is a vector space or not, check if it satisfies all the above properties. Calculation: Consider the set S = { A in V : each a i j is an integer } , The set can also be expressed as, S = [ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ] , a i j ∈ Z Since, the set S is a subset of matrices of dimension 3 × 4 and all the elements of the set satisfies the properties a1, a2, m1, m2, m3 and m4, So, the properties a1, a2, m1, m2, m3 and m4 will be satisfied by each vector of S as well

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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Chapter 5.2, Problem 16E

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Whether the subset S={A in V: each aij is an integer} of matrices of dimension 3×4 is a vector space.

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Chapter 5.2, Problem 15E

Chapter 5.2, Problem 17E

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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - Prob. 7E Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...

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Whether the subset S = { A in V : each a i j is an integer } of matrices of dimension 3 × 4 is a vector space.

Solution Summary: The author explains that the subset of matrices of dimension 3times 4 is a subspace if it satisfies all the following properties for u, v and w in

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Whether the subset S={A in V: each aij is an integer} of matrices of dimension 3×4 is a vector space.

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