### Related

##### columnspace-matrix-transpose-triangularize

A:matrix([7,0,1,3,2],...

B:transpose(A);

c:triangularize(B);

Calculate

##### columnspace-matrix

m:matrix([1,1],[-1,-1]);

columnspace(m);

Calculate

? columnspace;

Calculate

##### columnspace-matrix-nullspace

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

columnspace(A);

nullspace(A);

Calculate

##### columnspace-matrix-nullspace

m:matrix([15,9,-3,9],...

nullspace(m);

columnspace(m);

Calculate

##### columnspace-matrix-nullspace

m:matrix([15,9,-3,9],...

nullspace(m);

columnspace(m);

Calculate

##### columnspace-matrix-nullspace-transpose

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

nullspace(m);

a:transpose(m);

Calculate

##### columnspace-matrix

m:matrix([9,5,-4,2],[...

columnspace(m);

Calculate

##### columnspace-matrix-nullspace

m:matrix([15,9,-3,9],...

nullspace(m);

columnspace(m);

Calculate

##### columnspace-matrix

m:matrix([9,5,-4,2],[...

columnspace(m);

Calculate

### columnspace

Run Example
```(%i1)m:matrix([1,-1,2],[2,0,2],[1,3,-2],[1,4,-3]);
[ 1  - 1   2  ]
[             ]
[ 2   0    2  ]
(%o1)                           [             ]
[ 1   3   - 2 ]
[             ]
[ 1   4   - 3 ]
(%i2) nullspace(m);
[  2  ]
[     ]
(%o2)                            span([ - 2 ])
[     ]
[ - 2 ]
(%i3) a:transpose(m);
[  1   2   1    1  ]
[                  ]
(%o3)                        [ - 1  0   3    4  ]
[                  ]
[  2   2  - 2  - 3 ]
(%i4) columnspace(transpose(a));
[ - 1 ]  [ 1 ]
[     ]  [   ]
[  0  ]  [ 2 ]
(%o4)                        span([     ], [   ])
[  3  ]  [ 1 ]
[     ]  [   ]
[  4  ]  [ 1 ]
(%i5) ```
Run Example
```A:matrix([7,0,1,3,2],[8,9,3,7,0],[1,3,2,8,9]);
[ 7  0  1  3  2 ]
[               ]
(%o1)                          [ 8  9  3  7  0 ]
[               ]
[ 1  3  2  8  9 ]
(%i2) B:transpose(A);
[ 7  8  1 ]
[         ]
[ 0  9  3 ]
[         ]
(%o2)                             [ 1  3  2 ]
[         ]
[ 3  7  8 ]
[         ]
[ 2  0  9 ]
(%i3) columnspace(B);
[ 1 ]  [ 7 ]  [ 8 ]
[   ]  [   ]  [   ]
[ 3 ]  [ 0 ]  [ 9 ]
[   ]  [   ]  [   ]
(%o3)                      span([ 2 ], [ 1 ], [ 3 ])
[   ]  [   ]  [   ]
[ 8 ]  [ 3 ]  [ 7 ]
[   ]  [   ]  [   ]
[ 9 ]  [ 2 ]  [ 0 ]
(%i4) ```
Run Example
```m:matrix([1,2,3],[2,5,8],[2,1,0]);
[ 1  2  3 ]
[         ]
(%o1)                             [ 2  5  8 ]
[         ]
[ 2  1  0 ]
(%i2) columnspace(m);
[ 1 ]  [ 2 ]
[   ]  [   ]
(%o2)                         span([ 2 ], [ 5 ])
[   ]  [   ]
[ 2 ]  [ 1 ]
(%i3) ```

### Related Help

Help for Columnspace