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The Maxima on-line user's manual

Algebra Calculator

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Echelon Calculator

Echelon

Function: echelon (<M>) Returns the echelon form of the matrix <M>, as produced by Gaussian elimination. The echelon form is computed from <M> by elementary row operations such that the first non-zero element in each row in the resulting matrix is one and the column elements under the first one in each row are all zero.

A : matrix([ 1, 0, 1,0], [2, 1, -1,0], [0, 1, -1,0], [1, 2 ,1,0]);
echelon(A);
B: matrix([1,1,1],[-1,0,-2],[-3,-2,-4]);
echelon(B);
rank(B);

triangularize also carries out Gaussian elimination, but it does not normalize the leading non-zero element in each row.

lu_factor and cholesky are other functions which yield triangularized matrices.

          (%i1) M: matrix ([3, 7, aa, bb], [-1, 8, 5, 2], [9, 2, 11, 4]);
                                 [  3   7  aa  bb ]
                                 [                ]
          (%o1)                  [ - 1  8  5   2  ]
                                 [                ]
                                 [  9   2  11  4  ]
          (%i2) echelon (M);
                            [ 1  - 8  - 5      - 2     ]
                            [                          ]
                            [         28       11      ]
                            [ 0   1   --       --      ]
          (%o2)             [         37       37      ]
                            [                          ]
                            [              37 bb - 119 ]
                            [ 0   0    1   ----------- ]
                            [              37 aa - 313 ]

(%o1)                                true
(%i2) 

Echelon Example

Related Examples

echelon-matrix-rank-row

v1:[1,0,2];

v2:[-2,1,1];

v3:[0,1,5];

Calculate

echelon-matrix

a:matrix([2,1,1,a], [...

echelon(a);

Calculate

echelon-matrix-rank

/* El subespacio T={(...

s2:[2,5,3,1];

s3:[1,-1,-2,2];

Calculate

echelon-matrix-rank-row

v1:[1,2,3,4,5];

v2:[0,-1,1,2,3];

v3:[3,2,1,0,-1];

Calculate

echelon-matrix-rank

v1:[1,0,2];

v2:[-2,1,1];

v3:[0,1,5];

Calculate

echelon-matrix-rank

m:matrix([1,-4,7,a],[...

echelon(m);

rank(m);

Calculate

echelon-rank-row

V1:[1,2,3,4,5];

V2:[0,-1,1,2,3];

V3:[-4,-3,-2,-1,0];

Calculate

echelon-matrix-rank-transpose

/*Introducimos los ve...

v2:[0,-1,1,2,3];

v3:[3,2,1,0,-1];

Calculate

echelon-matrix

v1:[1,x];

v2:[2,y];

v3:[0,z];

Calculate

echelon-matrix-transpose

M: matrix ([a,1,a^2],...

N: matrix ([a,1],[1,a]);

A: echelon (M);

Calculate