Subspace generated by the columns of a matrix: colspace

### 5.47.14 Subspace generated by the columns of a matrix: colspace

The colspace command finds a basis for the column space of a matrix.

- colspace takes one mandatory argument and one optional argument:
  - A, a matrix.
  - Optionally, var, a variable name.
- colspace(A ⟨var⟩) returns a matrix whose columns are a basis of the subspace generated by the columns of A. With the optional argument var, Xcas will store the dimension of the subspace generated by the columns of A.

#### Examples

- 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