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  • Coordinate vector spaces

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  • Algebraic properties of R^n (or C^n)
  • Axioms of a vector space
  • Spans
  • Linear (in)dependence
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  • Subspaces
  • Geometric properties of R^n (or C^n)
  • Orthogonality and projection

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  • Definition of span of a set of vectors
  • Geometric description of span of a set of vectors in R^n (or C^n)
  • Determine if a particular set of vectors spans R^3
  • Determine if a particular vector is in the span of a set of vectors
  • Determine if a particular vector is in the span of a set of vectors in R^2
  • Determine if a particular vector is in the span of a set of vectors in R^3
  • The span of a set of vectors is a subspace
  • Definition of spanning/generating set for a space or subspace
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  1. Spans

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  • Definition of span of a set of vectorsClose match
  • Geometric description of span of a set of vectors in R^n (or C^n)Close match
  • The span of a set of vectors is a subspaceClose match
  • Definition of spanning/generating set for a space or subspaceClose match
  • Determine if a particular vector is in the span of a set of vectors in R^3Close match
  • Definition of subspace spanned by a set of a set of vectorsClose match
  • BasesClose match
  • Vector spacesClose match
  • SubspacesClose match
  • Linear combinationsClose match
  • Coordinate vector spacesClose match
  • Determine if a particular vector is in the span of a set of vectors in R^2Close match
  • Definition of linear combination of vectorsClose match
  • Definition of basis of a vector space (or subspace)Close match
  • DimensionClose match
  • The union of bases from independent subspaces is a basis for the space.Close match
  • Axioms of a vector spaceClose match
  • A set of nonzero vectors contains (as a subset) a basis for its span.Close match
  • A set of vectors containing fewer elements than the dimension of the space cannot spanClose match
  • Determine if a particular set of vectors spans R^3Close match

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