Lec 3 - Basis & Higher Dimensions
January 09, 2012
Q: How do
we find the smallest spanning 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.
a nice mathematical expression to define linear dependence?
Consider the equation
We have 3 equations
and 3 unknowns:
Sub into equation
Our set is linearly
order for a spanning set to be as small as possible, it must be linearly
in Higher Dimensions
For a set of
vectors to be closed under linear combinations, we must be able to apply the
operations of vector addition and scalar multiplication.
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