### 2.43.14 Subspace generated by the columns of a matrix : `colspace`

`colspace` takes as argument the matrix A of an linear application f with respect to the canonical basis.
`colspace` returns a matrix. The columns of this matrix are a basis of the subspace generated by the columns of A.
`colspace` may have a variable name as second argument, where `Xcas` will store the dimension of the subspace generated by the columns of A.
Input :

`colspace([[1,1,2],[2,1,3],[3,1,4]])`

Output :

`[[-1,0],[0,-1],[1,-2]]`

Input :

`colspace([[1,1,2],[2,1,3],[3,1,4]],dimension)`

Output :

`[[-1,0],[0,-1],[1,-2]]`

Then input:

`dimension`

Output :

`2`