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}
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