# Subspace generated by the rows of a matrix: rowspace

### 5.47.15 Subspace generated by the rows of a matrix: rowspace

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.

- Input:
  rowspace([[1,1,2],[2,1,3],[3,1,4]])
  Output:

  ⎡
  ⎢
  ⎣

  −1 | 0 | −1
  0 | −1 | −1

  ⎤
  ⎥
  ⎦

- Input:
  rowspace([[1,1,2],[2,1,3],[3,1,4]],dimension)
  Output:

  ⎡
  ⎢
  ⎣

  −1 | 0 | −1
  0 | −1 | −1

  ⎤
  ⎥
  ⎦

  then input:
  dimension
  Output:

  2