Linearly Dependent & Linearly Independent Set

Linearly Dependent Set:-                                                                   Let V be a vector space over the field F.A finite set {α1,α2,…………,αn} of vectors of V is said to be linearly dependent set if there exist         scalars a1,a2,……….,an  not all zero (some of them may be zero)such  that                                                                                                                      a1α1+a2α2+………..+anαn=0                                            
Linearly Independent Set:-                                                             Let V be a vector space over the field F then a finite set{α1,α2,……..αn} of vectors of V is said to be linearly independent if every relation of the form a1α1+a2α2+a3α3+………………….anαn,      a1,a2,…………….,anєF                                                                    ⇨             a1=0,a2=0,………………………..an=0                                                 Note:-                                                                                         An infinite set of the vectors of V is said to be linearly independent  if its every subset(finite set) is  linearly independent otherwise it is linearly dependent.