Definitions
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Vector space (ideally, try to remember all properties in 1.19:
distributive, commutative, associaive, and all the inverses)

Subspace

Sum of subspaces

Direct sum of subspaces

Linear combinaton

Span of a list of vectors

Finite and infinite-dimensional spaces

Linearly dependent and linearly independent lists of vectors

Basis

The dimension of a finite dimensional space

Linear map

Null space of an operator

Range of an operator

The matrix of a linear map



Things that require proofs (theorems, propositions, lemmas)
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(You are NOT required to remember theorems, lemmas, and propositions by
their number in the book)

Thms 1.44, 1.45, 2.7.

Linear dependence Lemma (please know the formulation) = Thm 2.21

Thms 2.23, 2.26, 2.31, 2.32, 2.33, 2.35, 2.43.

Thms 3.5, 3.14, 3.16, 3.19.