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  • Subspaces associated to a matrix

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  • Definition of matrix null space (right)
  • Definition of matrix null space (left)
  • Definition of column space of a matrix
  • The column space of an m-by-n matrix is a subspace of R^m (or C^m)
  • The pivot columns of a matrix are a basis for the column space.
  • Row operations do not necessarily preserve the column space.
  • The nonzero rows of the reduced row-echelon form of a matris are a basis for the row space.
  • Definition of row space of a matrix
  • Row equivalent matrices have the same row space.
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