i'm puzzled about vectors&matrices..

consider m vectors. You want to know if they're linear dependent. You can do that imposing their linear combination equal to zero and if you find the c1, c2, ...cn all equal to zero, then the vectors are independent. But there shoul be an easier way with determinants, but I am actually so confused, when detA=0 are the vectors dependent or independent?what about the rank?:confused: Can it help? I'm really puzzled...I know it would be too long to explain everything so if you could tell me a website where this things are explained in a straightforward way at least....thank you tons!