Section 1.3: Vector Equations

Abstract:

Vectors provide a wonderful way for us to write systems of equations compactly. You should already be familiar with two-d and three-d vectors from calculus classes. We now want to extend notions from those spaces into n-dimensional space. For example, vector addition is carried out component-wise.

The interesting new concept introduced in this section is that of span: roughly, the span of a set of vectors tex2html_wrap_inline499 is the subspace generated by linear combinations of the vectors tex2html_wrap_inline501 . The span represents the set of vectors tex2html_wrap_inline503 that can be solutions of the system

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Definition: A vector is a matrix with only a single column (``column vector''). The entries are called the components of the vector.

Example: #21, p. 38

Example: #27, p. 38



Wed Jan 23 11:39:28 EST 2008