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Echelon matrices
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Example of putting a matrix in echelon form
Example of putting a matrix in echelon form and identifying the pivot columns
Definition of (echelon matrix/matrix in (row) echelon form)
Gauss-Jordan procedure to put a matrix into reduced row echelon form
Example of (echelon matrix/matrix in (row) echelon form)
Definition of (row) echelon form of a matrix
Definition of matrix in reduced row echelon form
Definition of reduced row echelon form of a matrix
Definition of row reduce a matrix
Example of row reducing a 3-by-3 matrix
Example of row reducing a 4-by-4 matrix
Every matrix is row-equivalent to a matrix in reduced row echelon form.
Every matrix is row-equivalent to only one matrix in reduced row echelon form.
Definition of extended reduced row echelon form of a matrix
Theorem describing properties of the block matrices of the extended reduced row echelon form of a matrix
Theorem describing spaces associated to the block matrices of the extended reduced row echelon form of a matrix
Theorem describing the dimension of spaces associated to the block matrices of the extended reduced row echelon form of a matrix
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Echelon matrices
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Example of row reducing a 3-by-3 matrix
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