sentences:  This makes it possible to determine which columns are linearly independent by reducing only to echelon form.The above algorithm can be used in general to find the dependence relations between any set of vectors, and to pick out a basis from any spanning set.Also finding a basis for the column space of "A" is equivalent to finding a basis for the row space of the transpose matrix "A"T.
  
  To find the basis in a practical setting (e.g., for large matrices), the singular-value decomposition is typically used.