Question 106547
By definition 

Col(A)=Column Space of A=span{columns of A}


Remember a basis is a <b>linearly independent</b> set which <b>spans</b> the given subspace (which in this case is the column space of A).




Since the span the of the columns of A is Col(A), this means one of the two properties for a basis has been satisfied (that the set of vectors must span the column space of A)


So if we're assuming that the columns of A are linearly independent, this means the other property is satisfied (that a basis is linearly independent). 


 Since this assumption satisfies both of these properties, the columns of A forms a basis for Col(A) (that's if the columns of A are independent)