Q1Let V be the vector space over the field of real numbers consisting of allreal-valued sequences (a1, a2, a3, ...). Indicate, without proof, which ofthe following subsets of V is a vector space.(a) The set of all sequences satisfying a1 = a2 = a3.(b) The set of all sequences that are increasing, i.e., for whicha1 < a2 < az < …(c) The set of unbounded sequences.(d) The set of bounded sequences.(e) The set of sequences satisfying an+1 = an + an-1 for all n > 2.(f) The set of sequences satisfying an+1 = an × an-1 for all n > 2.Some comments:(1) You do not need to justify your answer, just write which of (a)-(f) arevector spaces and which are not.(ii) A sequence (a,)nz1 is said to be bounded if there is a real numberB > 0 (depending on the sequence) for which all a, lie in the interval[-B, B]. It is said to be unbounded otherwise.

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

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