January 06, 2012
Recall: A set of
vectors is closed under linear
combinations if we can take a linear combination of vectors in the set
and obtain a vector in the set.
In general: Sets of
vectors that are closed under linear combinations require only a small number
of vectors to describe the entire set.
How do we
find the smallest # of vectors needed in a spanning set?
vector equation of the plan is
Note: To find a
smallest spanning set, we need to identify when one vector the set is a linear
combination of the remaining vectors in the set.
A set of vectors is
linearly dependent if one
vector in the set is a linear combination of the remaining vectors.
Otherwise, the set
of vectors is linearly independent.
Created by Tim Pei with Microsoft OneNote 2010
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