### Related

##### echelon-genmatrix-lambda-random

a:genmatrix(lambda([x...

echelon(a);

a[2,3];

Calculate

v1:[1,2,-1];

v2:[3,-1,0];

v3:[4,1,-1];

Calculate

##### echelon-genmatrix-lambda-random

a:genmatrix(lambda([x...

echelon(a);

Calculate

##### echelon-is-matrix-transpose

A:matrix([1,0],[0,1]);

A-echelon(A);

B:transpose(A);

Calculate

listofvars(sqrt(1+sqr...

a: sqrt((sqrt(3-2*sqr...

Calculate

##### genmatrix

a[i,j]:=i^2-j^2;

A: genmatrix(a,2,3);

Calculate

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

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

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

Calculate

##### row-solve

uk_row: [2*x1-x2+3*x3...

solve (uk_row, [x1, x...

Calculate

##### random

a: 2+random(10);

blist: [-4,-3,-2,-1,1...

brand: 1+random(8);

Calculate

##### genmatrix-make_random_state-random

a[i,j]:=random(15);

a[2,17];

a[2,6];

Calculate

### [echelon,genmatrix,lambda,random,row]

Run Example
```(%i1)a:genmatrix(lambda([x,y], random(6)-random(6)),3,4);
[  2   - 3  3  0 ]
[                ]
(%o1)                         [ - 1  - 4  0  5 ]
[                ]
[ - 1  - 3  4  4 ]
(%i2) b:echelon(a);
[      3   3         ]
[ 1  - -   -     0   ]
[      2   2         ]
[                    ]
[           3     10 ]
(%o2)                       [ 0   1   - --  - -- ]
[           11    11 ]
[                    ]
[                 1  ]
[ 0   0    1    - -- ]
[                 47 ]
(%i3) b[2,3];
3
(%o3)                                - --
11
(%i4) matrix([0,0,0,0],-b[2,3] * list_matrix_entries(row(b,3)),[0,0,0,0]);
[ 0  0  0     0   ]
[                 ]
[       3      3  ]
(%o4)                         [ 0  0  --  - --- ]
[       11    517 ]
[                 ]
[ 0  0  0     0   ]
(%i5) ```
Run Example
```a:genmatrix(lambda([x,y], random(2)-random(2)),3,4);
[  0   - 1  - 1  0 ]
[                  ]
(%o1)                        [ - 1   0    0   1 ]
[                  ]
[  1    1    0   0 ]
(%i2) b:echelon(a);
[ 1  0  0  - 1 ]
[              ]
(%o2)                          [ 0  1  1   0  ]
[              ]
[ 0  0  1  - 1 ]
(%i3) c:b+matrix([0,0,0,0],-b[2,3] * list_matrix_entries(row(b,3)),[0,0,0,0]);
[ 1  0  0  - 1 ]
[              ]
(%o3)                          [ 0  1  0   1  ]
[              ]
[ 0  0  1  - 1 ]
(%i4) d:c+matrix(-c[1,2]*list_matrix_entries(row(c,2))+ -c[1,3]*list_matrix_entries(row(c,3)),[0,0,0,0],[0,0,0,0]);
[ 1  0  0  - 1 ]
[              ]
(%o4)                          [ 0  1  0   1  ]
[              ]
[ 0  0  1  - 1 ]
(%i5) ```
Run Example
```a:genmatrix(lambda([x,y], random(3)-random(3)),3,4);
[  2    0   0  0 ]
[                ]
(%o1)                         [ - 1  - 1  0  2 ]
[                ]
[ - 1   0   1  1 ]
(%i2) b:echelon(a);
[ 1  0  0   0  ]
[              ]
(%o2)                          [ 0  1  0  - 2 ]
[              ]
[ 0  0  1   1  ]
(%i3) c:b+matrix([0,0,0,0],-b[2,3] * list_matrix_entries(row(b,3)),[0,0,0,0]);
[ 1  0  0   0  ]
[              ]
(%o3)                          [ 0  1  0  - 2 ]
[              ]
[ 0  0  1   1  ]
(%i4) d:c+matrix(-c[1,2]*list_matrix_entries(row(c,2))+ -c[1,3]*list_matrix_entries(row(c,3)),[0,0,0,0],[0,0,0,0]);
[ 1  0  0   0  ]
[              ]
(%o4)                          [ 0  1  0  - 2 ]
[              ]
[ 0  0  1   1  ]
(%i5) ```

### Related Help

Help for Echelon

Help for Genmatrix

Help for Lambda

Help for Random

Help for Row