> with(LinearAlgebra);

  [Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix,

        BidiagonalForm, BilinearForm, CharacteristicMatrix,

        CharacteristicPolynomial, Column, ColumnDimension,

        ColumnOperation, ColumnSpace, CompanionMatrix,

        ConditionNumber, ConstantMatrix, ConstantVector,

        CreatePermutation, CrossProduct, DeleteColumn, DeleteRow,

        Determinant, DiagonalMatrix, Dimension, Dimensions,

        DotProduct, Eigenvalues, Eigenvectors, Equal,

        ForwardSubstitute, FrobeniusForm, GenerateEquations,

        GenerateMatrix, GetResultDataType, GetResultShape,

        GivensRotationMatrix, GramSchmidt, HankelMatrix, HermiteForm,

        HermitianTranspose, HessenbergForm, HilbertMatrix,

        HouseholderMatrix, IdentityMatrix, IntersectionBasis,

        IsDefinite, IsOrthogonal, IsSimilar, IsUnitary,

        JordanBlockMatrix, JordanForm, LA_Main, LUDecomposition,

        LeastSquares, LinearSolve, Map, Map2, MatrixAdd,

        MatrixInverse, MatrixMatrixMultiply, MatrixNorm,

        MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial,

        Minor, Multiply, NoUserValue, Norm, Normalize, NullSpace,

        OuterProductMatrix, Permanent, Pivot, QRDecomposition,

        RandomMatrix, RandomVector, Rank, Row, RowDimension,

        RowOperation, RowSpace, ScalarMatrix, ScalarMultiply,

        ScalarVector, SchurForm, SingularValues, SmithForm, SubMatrix,

        SubVector, SumBasis, SylvesterMatrix, ToeplitzMatrix, Trace,

        Transpose, TridiagonalForm, UnitVector, VandermondeMatrix,

        VectorAdd, VectorAngle, VectorMatrixMultiply, VectorNorm,

        VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip]

> A := Matrix(3,4,[[1,2,1,3],[3,-1,-3,-1],[2,3,1,4]]);

                           [1     2     1     3]
                           [                   ]
                      A := [3    -1    -3    -1]
                           [                   ]
                           [2     3     1     4]

> RowOperation(A,[2,1],-3);

                        [1     2     1      3]
                        [                    ]
                        [0    -7    -6    -10]
                        [                    ]
                        [2     3     1      4]

> read("/afs/eos.ncsu.edu/users/k/kaltofen/www/courses/LinAlgebra/Maple/
> RefPkg/InitPkg.mpl");

  libname := /afs/eos.ncsu.edu/users/k/kaltofen/www/courses/LinAlg\

        ebra/Maple, "/afs/bp/dist/maple60/lib"

> with(RefPkg);

                                [Ref]

> Ref(A);

                      [1     2     1       3  ]
                      [                       ]
                      [0    -7     -6     -10 ]
                      [                       ]
                      [0     0    -1/7    -4/7]

> infolevel['RefPkg']:=3;

                        infolevel[RefPkg] := 3

> Ref(A);

                          Searching column 1


                  Added row 1 times , -3,  to row 2


                        [1     2     1      3]
                        [                    ]
                        [0    -7    -6    -10]
                        [                    ]
                        [2     3     1      4]


                  Added row 1 times , -2,  to row 3


                        [1     2     1      3]
                        [                    ]
                        [0    -7    -6    -10]
                        [                    ]
                        [0    -1    -1     -2]


                          Searching column 2


                 Added row 2 times , -1/7,  to row 3


                      [1     2     1       3  ]
                      [                       ]
                      [0    -7     -6     -10 ]
                      [                       ]
                      [0     0    -1/7    -4/7]


                      [1     2     1       3  ]
                      [                       ]
                      [0    -7     -6     -10 ]
                      [                       ]
                      [0     0    -1/7    -4/7]

>