Echelon

If a matrix is in echelon form, the nonzero rows form a basis for the row space.

Row-addition

Applying elementary row-addition operations does not change the row space.

find a basis

To find basis for row space of a matrix A, iteratively transform A into a matrix B

• in echelon form
• with no zero rows
• whose row space is the same as that of A.

See Gaussian elimination - Finding a basis for the computation