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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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The nonzero rows of the reduced row-echelon form of a matris are a basis for the row space.
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Subspaces associated to a matrix