Linear Algebra by Reg Allenby

Author:Reg Allenby [Allenby, R B J T]
Language: eng
Format: epub
ISBN: 978-0-08-057179-9
Publisher: Elsevier Science
Published: 1995-04-18T04:00:00+00:00

Example 4 (i)–(iii) and (v)–(vii) exhibit finite spanning sets – (iv) shows an infinite spanning set (where no finite spanning set is possible, as you should have discovered in answering Tutorial Problem 7.1.)

TUTORIAL PROBLEM 7.2

(a) Do you think that 4 could be spanned by just three (carefully chosen) vectors?

(b) What set spans the trivial subspace {(0, 0, 0, 0)} of 4?

The above comments lead, naturally, to the following definition.

• Definition 4

If a vector space V is spanned by a finite set of vectors we say that V is finite dimensional.

[Many important vector spaces are not finite dimensional; see, for example, Exercise 35 below.]

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