Im having trouble under stand the relationships between determinats, span, basis. Given a 3x3 matrix on R3 vector space. * If determinat is 0, it is linearly dependent, will NOT span R3, is NOT a basis of R3. , If determinant is non-zero, its linearly independent, will span R3, is a basis of R3 I was not able to confirm this statment one of my friends said, and i checked wiki as well, but didn't find a answer. Question is, is this right? can anyone confirm this? Thanks in advance.