Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Question
8.1 Which of the following statements about linear vector spaces are true? Where a statement is false, give a counter-example to demonstrate this. (a) Non-singular N x N matrices form a vector space of dimension N2 (b) Singular N x N matrices form a vector space of dimension N2 (c) Complex numbers form a vector space of dimension 2. (d) Polynomial functions of x form an infinite-dimensional vector space. (e): Series-d07a。( …ndly for which, N 0 Oly 2 1 forman N-dimensional vector space (f) Absolutely convergent series form an infinite-dimensional vector space. (g) Convergent series with terms of alternating sign form an infinite-dimensional vector space.
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Transcribed Image Text:8.1 Which of the following statements about linear vector spaces are true? Where a statement is false, give a counter-example to demonstrate this. (a) Non-singular N x N matrices form a vector space of dimension N2 (b) Singular N x N matrices form a vector space of dimension N2 (c) Complex numbers form a vector space of dimension 2. (d) Polynomial functions of x form an infinite-dimensional vector space. (e): Series-d07a。( …ndly for which, N 0 Oly 2 1 forman N-dimensional vector space (f) Absolutely convergent series form an infinite-dimensional vector space. (g) Convergent series with terms of alternating sign form an infinite-dimensional vector space.
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