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Student[LinearAlgebra][GaussianElimination] - perform Gaussian elimination on a Matrix
Student[LinearAlgebra][ReducedRowEchelonForm] - perform Gauss-Jordan elimination on a Matrix
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Calling Sequence
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GaussianElimination(A)
ReducedRowEchelonForm(A)
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Description
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The GaussianElimination(A) command performs Gaussian elimination on the Matrix A and returns the upper triangular factor U with the same dimensions as A.
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This command is equivalent to calling LUDecomposition with the output=['U'] option.
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The ReducedRowEchelonForm(A) command performs Gauss-Jordan elimination on the Matrix A and returns the unique reduced row echelon form R of A.
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This command is equivalent to calling LUDecomposition with the output=['R'] option.
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Examples
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![with(Student[LinearAlgebra])](/support/helpjp/helpview.aspx?si=4086/file04990/math94.png)
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![A := Matrix([[8, 4, -5, -5], [3, -5, 8, 5], [-1, 0, 3, -4], [-5, -2, -1, -9]])](/support/helpjp/helpview.aspx?si=4086/file04990/math101.png)
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](/support/helpjp/helpview.aspx?si=4086/file04990/math108.png)
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![Matrix([[8, 4, -5, -5], [0, -13/2, 79/8, 55/8], [0, 0, 163/52, -213/52], [0, 0, 0, -2607/163]])](/support/helpjp/helpview.aspx?si=4086/file04990/math115.png)
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![Matrix([[1, 0, 0, 0, 1715/2607], [0, 1, 0, 0, -3668/2607], [0, 0, 1, 0, -1345/869], [0, 0, 0, 1, 1759/2607]])](/support/helpjp/helpview.aspx?si=4086/file04990/math122.png)
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