### 15.1.13 Subspace generated by the rows of a matrix

The rowspace command finds a basis for the row space of a matrix.

- rowspace takes one mandatory argument and one optional argument:
  - A, a matrix.
  - Optionally, var, a variable name.
- rowspace(A⟨,var⟩) returns a list of vectors which form a basis of the subspace generated by the rows of A. With the optional argument var, Xcas will store the dimension of the subspace generated by the rows of A.

#### Examples

rowspace([[1,1,2],[2,1,3],[3,1,4]])

⎡
⎢
⎣

−1 | 0 | −1
0 | −1 | −1

⎤
⎥
⎦

rowspace([[1,1,2],[2,1,3],[3,1,4]],dimension)

⎡
⎢
⎣

−1 | 0 | −1
0 | −1 | −1

⎤
⎥
⎦

dimension

2 |  |  |  |  |  |  |  |  |  |