Math Forum :: View topic – questions

why the vectors are linear dependent, then det =0 , why there will be infinitely many solution of the system? why linear independent, then det not =0 (unique solution), what are the relationships between them?
also, why{ r1, r2, r3, r4} are four vectors in R^3 , then{r1, r2, r3, r4 }are linear dependent? thx~