### Related

##### echelon-matrix

A:matrix([2,-1,0,0,0]...

B:echelon(A);

B;

Calculate

##### echelon-matrix

a:matrix([1,1,3,-5],[...

echelon(a);

Calculate

v1:[1,0,2];

v2:[-2,1,1];

v3:[0,1,5];

Calculate

##### echelon-matrix

M: matrix ([1, 2, 0, ...

echelon (M);

Calculate

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

/*Introducimos los ve...

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

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

Calculate

##### echelon-linsolve-matrix-rank

/* El subespacio T={(...

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

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

Calculate

v1:[1,0,1];

v2:[1,1,0];

v3:[0,1,1];

Calculate

##### echelon-matrix-transpose

f(x,y,z):=[z+y,-x+y-z...

mf:transpose(matrix(f...

imagen:matrix(f(1,0,0...

Calculate

##### echelon-matrix

m:matrix([1,-1,2],[1,...

echelon(m);

Calculate

v1:[-1,0,1];

v2:[0,1,-1];

v3:[4,-2,1];

Calculate

### echelon

Run Example
```(%i1)A:matrix([1,1,1,1],[-1,1,1,-1], [1,0,1,0],[0,-1,0,1]);
[  1    1   1   1  ]
[                  ]
[ - 1   1   1  - 1 ]
(%o1)                        [                  ]
[  1    0   1   0  ]
[                  ]
[  0   - 1  0   1  ]
(%i2) echA:echelon(A);
[ 1  0  1   0  ]
[              ]
[ 0  1  0   1  ]
(%o2)                          [              ]
[ 0  0  1  - 1 ]
[              ]
[ 0  0  0   1  ]
(%i3) A1:invert(A);
[      1   1     1 ]
[ 0  - -   -   - - ]
[      2   2     2 ]
[                  ]
[ 1         1    1 ]
[ -   0   - -  - - ]
[ 2         2    2 ]
(%o3)                        [                  ]
[     1    1    1  ]
[ 0   -    -    -  ]
[     2    2    2  ]
[                  ]
[ 1         1   1  ]
[ -   0   - -   -  ]
[ 2         2   2  ]
(%i4) A1.A;
[ 1  0  0  0 ]
[            ]
[ 0  1  0  0 ]
(%o4)                           [            ]
[ 0  0  1  0 ]
[            ]
[ 0  0  0  1 ]
(%i5) ```
Run Example
```A: matrix ([5,2,-1],[-1,-2,-3],[-8,-3,2],[3,-1,5]);
[  5    2   - 1 ]
[               ]
[ - 1  - 2  - 3 ]
(%o1)                          [               ]
[ - 8  - 3   2  ]
[               ]
[  3   - 1   5  ]
(%i2) echelon(A);
[    2    1 ]
[ 1  -  - - ]
[    5    5 ]
[           ]
(%o2)                            [ 0  1   2  ]
[           ]
[ 0  0   1  ]
[           ]
[ 0  0   0  ]
(%i3) ```
Run Example
```c:matrix([1/R1+1/R12+1/R13,-1/R12,-1/R13, I0],[-1/R12,1/R2+1/R23+1/R12,-1/R23, I0],[-1/R13,-1/R23,1/R3+1/R13+1/R23, I0]);
[  1     1    1          1               1           ]
[ --- + --- + --      - ---           - ---       I0 ]
[ R13   R12   R1        R12             R13          ]
[                                                    ]
[        1         1    1     1          1           ]
(%o1)       [     - ---       --- + -- + ---      - ---       I0 ]
[       R12       R23   R2   R12        R23          ]
[                                                    ]
[        1               1        1     1     1      ]
[     - ---           - ---       -- + --- + ---  I0 ]
[       R13             R23       R3   R23   R13     ]
(%i2) d:echelon(c);
R1 R13                     R1 R12
(%o2) matrix([1, - -----------------------, - -----------------------,
(R12 + R1) R13 + R1 R12    (R12 + R1) R13 + R1 R12
I0 R1 R12 R13
-----------------------], [0, 1, - (((R12 + R1) R23 + (R12 + R1) R13 + R1 R12)
(R12 + R1) R13 + R1 R12
R3 + ((R12 + R1) R13 + R1 R12) R23)/((R1 R23 + (R12 + R1) R13 + R1 R12) R3),
((I0 R12 + I0 R1) R13 + 2 I0 R1 R12) R23
- ----------------------------------------],
R1 R23 + (R12 + R1) R13 + R1 R12
[0, 0, 1, ((((I0 R13 + 3 I0 R1) R2 + (I0 R12 + I0 R1) R13 + 2 I0 R1 R12) R23
+ ((2 I0 R12 + 3 I0 R1) R13 + 3 I0 R1 R12) R2) R3)
/(((R2 + R12 + R1) R23 + (R13 + R12) R2 + (R12 + R1) R13 + R1 R12) R3
+ ((R13 + R1) R2 + (R12 + R1) R13 + R1 R12) R23
+ ((R12 + R1) R13 + R1 R12) R2)])
(%i3) fortran(d[3,4]);
(((I0*R13+3*I0*R1)*R2+(I0*R12+I0*R1)*R13+2*I0*R1*R12)*R23+((2*I0*R
1   12+3*I0*R1)*R13+3*I0*R1*R12)*R2)*R3/(((R2+R12+R1)*R23+(R13+R12)
2   *R2+(R12+R1)*R13+R1*R12)*R3+((R13+R1)*R2+(R12+R1)*R13+R1*R12)*R
3   23+((R12+R1)*R13+R1*R12)*R2)
(%o3)                                done
(%i4) e:matrix([1/R1+1/R12+1/R13,-1/R12,-1/R13, I0],[-1/R12,1/R2+1/R23+1/R12,-1/R23, 0],[-1/R13,-1/R23,1/R3+1/R13+1/R23, 0]);
[  1     1    1          1               1           ]
[ --- + --- + --      - ---           - ---       I0 ]
[ R13   R12   R1        R12             R13          ]
[                                                    ]
[        1         1    1     1          1           ]
(%o4)       [     - ---       --- + -- + ---      - ---       0  ]
[       R12       R23   R2   R12        R23          ]
[                                                    ]
[        1               1        1     1     1      ]
[     - ---           - ---       -- + --- + ---  0  ]
[       R13             R23       R3   R23   R13     ]
(%i5) ```

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