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