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Row equivalence is an equivalence relation
Definition of row operations on a matrix
Definition of pivot
Definition of pivot column
Definition of pivot position
Definition of row equivalent matrices
Definition of leading entry in a row of a matrix

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Definition of pivot column

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Definition of pivotClose match
Definition of pivot positionClose match
The pivot columns of a matrix are a basis for the column space.Close match
Example of putting a matrix in echelon form and identifying the pivot columnsClose match
Row operations do not necessarily preserve the column space.Close match
Example of (echelon matrix/matrix in (row) echelon form)Close match
The reduced row-echelon form of a matrix determines which subset of a spanning set is a basis.Close match
Definition of (row) echelon form of a matrixClose match
Definition of (echelon matrix/matrix in (row) echelon form)Close match
Echelon matricesClose match
The number of pivots in the reduced row echelon form of a consistent system determines the number of free variables in the solution set.Close match
The rank of a matrix equals number of pivots in a reduced row echelon form.Close match
Definition of basic/dependent/leading variable in a linear systemClose match
Definition of echelon form of a linear systemRelated
Definition of leading entry in a row of a matrixRelated
Algorithm for computing an LU decompositionRelated
Definition of column space of a matrixRelated
Definition of row operations on a matrixRelated
Row equivalence is an equivalence relationRelated
Row equivalent matrices have the same row space.Related

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