### Related

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

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

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

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

##### echelon-matrix-rank-row-transpose

/*Introducimos los ve...

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

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

Calculate

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

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

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

Calculate

### [echelon,matrix,rank,row,transpose]

Run Example
```(%i1)v1:[1,2,3,4,5];
(%o1)                           [1, 2, 3, 4, 5]
(%i2) v2:[0,-1,1,2,3];
(%o2)                          [0, - 1, 1, 2, 3]
(%i3) v3:[3,2,1,0,-1];
(%o3)                          [3, 2, 1, 0, - 1]
(%i4) v4:[-4,-3,-2,-1,0];
(%o4)                       [- 4, - 3, - 2, - 1, 0]
(%i5) m:matrix(v1,v2,v3,v4);
[  1    2    3    4    5  ]
[                         ]
[  0   - 1   1    2    3  ]
(%o5)                     [                         ]
[  3    2    1    0   - 1 ]
[                         ]
[ - 4  - 3  - 2  - 1   0  ]
(%i6) rank(m);
(%o6)                                  3
(%i7) n:echelon(m);
[    2   1          1 ]
[ 1  -   -    0   - - ]
[    3   3          3 ]
[                     ]
[ 0  1  - 1  - 2  - 3 ]
(%o7)                       [                     ]
[             5    7  ]
[ 0  0   1    -    -  ]
[             3    3  ]
[                     ]
[ 0  0   0    0    0  ]
(%i8) w1:row(n,1);
[    2  1       1 ]
(%o8)                         [ 1  -  -  0  - - ]
[    3  3       3 ]
(%i9) w2:row(n,2);
(%o9)                       [ 0  1  - 1  - 2  - 3 ]
(%i10) w3:row(n,3);
[          5  7 ]
(%o10)                         [ 0  0  1  -  - ]
[          3  3 ]
(%i11) n:newma:matrix([1,2/3,1/3,0,-1/3],[0,1,-1,-2,-3],[0,0,1,5/3,7/3],[0,0,0,0,0],[x,y,z,t,e]);
[    2   1          1 ]
[ 1  -   -    0   - - ]
[    3   3          3 ]
[                     ]
[ 0  1  - 1  - 2  - 3 ]
[                     ]
(%o11)                      [             5    7  ]
[ 0  0   1    -    -  ]
[             3    3  ]
[                     ]
[ 0  0   0    0    0  ]
[                     ]
[ x  y   z    t    e  ]
(%i12) transpose(n);
[  1    0   0  0  x ]
[                   ]
[  2                ]
[  -    1   0  0  y ]
[  3                ]
[                   ]
[  1                ]
[  -   - 1  1  0  z ]
(%o12)                       [  3                ]
[                   ]
[           5       ]
[  0   - 2  -  0  t ]
[           3       ]
[                   ]
[   1       7       ]
[ - -  - 3  -  0  e ]
[   3       3       ]
(%i13) ```
Run Example
```/*Introducimos los vectores*/v1:[1,2,3,4,5];
(%o1)                           [1, 2, 3, 4, 5]
(%i2) v2:[0,-1,1,2,3];
(%o2)                          [0, - 1, 1, 2, 3]
(%i3) v3:[3,2,1,0,-1];
(%o3)                          [3, 2, 1, 0, - 1]
(%i4) v4:[-4,-3,-2,-1,0];
(%o4)                       [- 4, - 3, - 2, - 1, 0]
(%i5) /*Definimos la matriz m*/m:matrix(v1,v2,v3,v4);
[  1    2    3    4    5  ]
[                         ]
[  0   - 1   1    2    3  ]
(%o5)                     [                         ]
[  3    2    1    0   - 1 ]
[                         ]
[ - 4  - 3  - 2  - 1   0  ]
(%i6) /*Calculamos el rango*/rank(m);
(%o6)                                  3
(%i7) /*Reducimos la matriz para conocer la base*/m1:echelon(m);
[    2   1          1 ]
[ 1  -   -    0   - - ]
[    3   3          3 ]
[                     ]
[ 0  1  - 1  - 2  - 3 ]
(%o7)                       [                     ]
[             5    7  ]
[ 0  0   1    -    -  ]
[             3    3  ]
[                     ]
[ 0  0   0    0    0  ]
(%i8) /*cargamos la base en memoria*/base:matrix(v1,v2,v3);
[ 1   2   3  4   5  ]
[                   ]
(%o8)                        [ 0  - 1  1  2   3  ]
[                   ]
[ 3   2   1  0  - 1 ]
(%i9) /*cargamos el vector LD a cualquier opción del sistema*/v5:[x,y,z,s,t];
(%o9)                           [x, y, z, s, t]
(%i10) /*si dim=5 y rango=3 =>
Ec.Imp = 2*//*Se plantea la matriz general calcular los dos determinantes*/mg:matrix(v1,v2,v3,v5);
[ 1   2   3  4   5  ]
[                   ]
[ 0  - 1  1  2   3  ]
(%o10)                       [                   ]
[ 3   2   1  0  - 1 ]
[                   ]
[ x   y   z  s   t  ]
(%i11) /*trasponemos la matriz para preparar los determinantes*/mg_traspuesta:transpose(mg);
[ 1   0    3   x ]
[                ]
[ 2  - 1   2   y ]
[                ]
(%o11)                        [ 3   1    1   z ]
[                ]
[ 4   2    0   s ]
[                ]
[ 5   3   - 1  t ]
(%i12) /*cargamos en RAM las variables de cada fila de mg_traspuesta*/ec_x:row(mg_traspuesta,1);
(%o12)                          [ 1  0  3  x ]
(%i13) ec_y:row(mg_traspuesta,2);
(%o13)                         [ 2  - 1  2  y ]
(%i14) ec_z:row(mg_traspuesta,3);
(%o14)                          [ 3  1  1  z ]
(%i15) ec_s:row(mg_traspuesta,4);
(%o15)                          [ 4  2  0  s ]
(%i16) ec_t:row(mg_traspuesta,5);
(%o16)                         [ 5  3  - 1  t ]
(%i17) ```
Run Example
```/*Introducimos los vectores*/v1:[1,2,3,4,5];
(%o1)                           [1, 2, 3, 4, 5]
(%i2) v2:[0,-1,1,2,3];
(%o2)                          [0, - 1, 1, 2, 3]
(%i3) v3:[3,2,1,0,-1];
(%o3)                          [3, 2, 1, 0, - 1]
(%i4) v4:[-4,-3,-2,-1,0];
(%o4)                       [- 4, - 3, - 2, - 1, 0]
(%i5) /*Definimos la matriz m*/m:matrix(v1,v2,v3,v4);
[  1    2    3    4    5  ]
[                         ]
[  0   - 1   1    2    3  ]
(%o5)                     [                         ]
[  3    2    1    0   - 1 ]
[                         ]
[ - 4  - 3  - 2  - 1   0  ]
(%i6) /*Calculamos el rango*/rank(m);
(%o6)                                  3
(%i7) /*Reducimos la matriz para conocer la base*/m1:echelon(m);
[    2   1          1 ]
[ 1  -   -    0   - - ]
[    3   3          3 ]
[                     ]
[ 0  1  - 1  - 2  - 3 ]
(%o7)                       [                     ]
[             5    7  ]
[ 0  0   1    -    -  ]
[             3    3  ]
[                     ]
[ 0  0   0    0    0  ]
(%i8) /*cargamos la base en memoria*/base:matrix(v1,v2,v3);
[ 1   2   3  4   5  ]
[                   ]
(%o8)                        [ 0  - 1  1  2   3  ]
[                   ]
[ 3   2   1  0  - 1 ]
(%i9) /*cargamos el vector LD a cualquier opción del sistema*/v5:[x,y,z,s,t];
(%o9)                           [x, y, z, s, t]
(%i10) /*si dim=5 y rango=3 =>
Ec.Imp = 2*//*Se plantea la matriz general calcular los dos determinantes*/mg:matrix(v1,v2,v3,v5);
[ 1   2   3  4   5  ]
[                   ]
[ 0  - 1  1  2   3  ]
(%o10)                       [                   ]
[ 3   2   1  0  - 1 ]
[                   ]
[ x   y   z  s   t  ]
(%i11) /*trasponemos la matriz para preparar los determinantes*/mg_traspuesta:transpose(mg);
[ 1   0    3   x ]
[                ]
[ 2  - 1   2   y ]
[                ]
(%o11)                        [ 3   1    1   z ]
[                ]
[ 4   2    0   s ]
[                ]
[ 5   3   - 1  t ]
(%i12) /*cargamos en RAM las variables de cada fila de mg_traspuesta*/ec1_x:row(mg_traspuesta,1);
(%o12)                          [ 1  0  3  x ]
(%i13) ec1_z:row(mg_traspuesta,1);
(%o13)                          [ 1  0  3  x ]
(%i14) ec1_s:row(mg_traspuesta,1);
(%o14)                          [ 1  0  3  x ]
(%i15) ec1_t:row(mg_traspuesta,1);
(%o15)                          [ 1  0  3  x ]
(%i16) ```

### Related Help

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