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Figure 5.4.3
The following key definition will make the preceding ideas more precise and enable us to extend the concept of a coordinate
system to general vector spaces.
DEFINITION is a set of vectors in V, then S is called a basis for V if the following two
If V is any vector space and
conditions hold:
(a) S is linearly independent.
(b) S spans V.
A basis is the vector space generalization of a coordinate system in 2-space and 3-space. The following theorem will help us to see
why this is so.
THEOREM 5.4.1
