The Maxima on-line user's manual

Algebra 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.

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)

Related Examples

echelon-matrix-rank-transpose

/*Introducimos los ve...

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

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

Calculate

echelon-matrix-rank

/* El subespacio T={(...

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

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

Calculate

echelon-matrix-rank-row

m:matrix([1,2,3,4,5],...

rank(m);

mr:echelon(m);

Calculate

echelon-matrix-rank-row

/*En primer lugar int...

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

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

Calculate

echelon-matrix

v1:[1,2,0,1];

n:matrix (v1,[x,y,z,t]);

echelon(n);

Calculate

echelon-matrix-rank

/*Comprobemos que B e...

rank(m);

n:echelon(m);

Calculate

v1:[1, 0, 2];

v2:[−2, 1, 1];

v3:[0, 1, 5];

Calculate

echelon-matrix

m:matrix([[4,2,b+1,3]...

mg:echelon(m);

Calculate

echelon-matrix

M: matrix ([0,5,4,7],...

echelon (M);

Calculate

echelon-matrix

echelon(matrix([1,1,1...

Calculate