Linear combination & Linear Span

Linear Combination Of Vectors:-                                                         Let V be a vector space over the field F,then a vector αєV is said to be a linear combination of vectors α1,α2,α3,………………..αnєV                  If     α=a1α1+a2α2+a3α3+…………………………+anαn                                       where  a1,a2,a3,……………………………….anєF                          
Linear Span Of A Set:-                                                                  Let V be a vector space over the field F,S be a non-empty subset of V,then the set of all linear combinations of finite number elements of S is called linear combinations of finite number elements of S is  called linear span of S and is denoted by L(S).                                                        Thus,                                                                    L(S)={a1α1+a2α2+…………+anαn :α1,α2,……………αnєS,a1,…,anєF}