I have come across a theorem which says that det(A)=0 if and only if the row (or column) vectors of A are linearly dependent. I can understand the proof for it, but fails to figure out what's the essential meaning of this theorem. Can someone provide me a simple intuitutive understanding of this theorem? By intitutive understanding, I mean something that one can assure himself of some result without doing much derivation. Thanks in advance!