3.1 Introduction

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Throughout this chapter, we will be studying Fn, the set of all n{dimensional

column vectors with components from a ¯eld F. We continue our study of

matrices by considering an important class of subsets of F n called subspaces.

These arise naturally for example, when we solve a system of m linear ho-

mogeneous equations in n unknowns.

We also study the concept of linear dependence of a family of vectors.

This was introduced brie°y in Chapter 2, Remark 2.5.4. Other topics dis-

cussed are the row space, column space and null space of a matrix over F,

the dimension of a subspace, particular examples of the latter being the rank

and nullity of a matrix.

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