Concept explainers
True or False? In Exercises 49 and 50, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) To show that a set is not a
(b) The set of all first-degree polynomials with the standard operations is a vector space.
(c) The set of all pairs of real numbers of the form
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Elementary Linear Algebra (MindTap Course List)
- True or False? In Exercises 83-86, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a The set of all n-tuples is n-space and is denoted by Rn. b The additive identity of a vector space is not unique. c Once a theorem has been proved for an abstract vector space, you need not give separate proofs for n-tuples, matrices, and polynomials.arrow_forwardTesting for a Vector Space In Exercises 13-36, determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails. M4,6arrow_forwardTesting for a Vector Space In Exercises 13-36, determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails. The set of all quadratic functions whose graphs pass through the origin.arrow_forward
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- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning