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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.
  • Nonzero rows of reduced row-echelon form give 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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  1. Row operations do not necessarily preserve the column space.

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  • The pivot columns of a matrix are a basis for the column space.Close match
  • Row equivalent matrices have the same row space.Close match
  • The row space of a matrix is a vector spaceClose match
  • The column space of a matrix is a vector spaceClose match
  • Definition of row space of a matrixClose match
  • Nonzero rows of reduced row-echelon form give a basis for the row spaceClose match
  • Definition of pivot columnClose match
  • The reduced row-echelon form of a matrix determines which subset of a spanning set is a basis.Close match
  • Subspaces associated to a matrixClose match
  • The column space of an m-by-n matrix is a subspace of R^m (or C^m)Close match
  • Row operationsClose match
  • Definition of column space of a matrixClose match
  • Example of putting a matrix in echelon form and identifying the pivot columnsClose match
  • Definition of pivotClose match
  • Definition of row operations on a matrixClose match
  • Definition of row equivalent matricesClose match
  • Definition of pivot positionClose match
  • Row equivalence is an equivalence relationClose match
  • An eigenspace of a matrix is the null space of a related matrix.Related
  • Subspaces associated to a linear transformationRelated

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