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9: Subspaces and Spanning Sets

Last updated

Mar 5, 2021
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- 8.5: Review Problems
- 9.1: Subspaces

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It is time to study vector spaces more carefully and return to some fundamental questions:

$\textit{Subspaces}$ : When is a subset of a vector space itself a vector space? (This is the notion of a $\textit{subspace}$ .)
$\textit{Linear Independence}$ : Given a collection of vectors, is there a way to tell whether they are independent, or if one is a "linear combination'' of the others?
$\textit{Dimension}$ : Is there a consistent definition of how "big'' a vector space is?
$\textit{Basis}$ : How do we label vectors? Can we write any vector as a sum of some basic set of vectors? How do we change our point of view from vectors labelled one way to vectors labelled in another way

Let's start at the top!

9.1: Subspaces
A subspace of a vector space V is a subset U under the inherited addition and scalar multiplication operations of V .
9.2: Building Subspaces
9.3: Review Problems

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David Cherney, Tom Denton, and Andrew Waldron (UC Davis)

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