Linear Independence There are inefficient(too big)spanning sets for a vector space V.For example {(1,0),(0,1),(1,1)}is a spanning set for R2 but any two of the three vectors still spans. Dependence Relation Let v1,v2,...,UnE V.Then a dependence relation between V1,U2,...,Un is an equation c1v1+c2v2+...+CnUn =0,C1,C2,...Cn ER. The dependence relation is said to the trivial dependence relation if all the cs are zero.So in the above 1(1,0)+1(0,1)-1(1,1)=0. is a dependence relation. 4口+++左+4生+定QCLinear Independence There are inefficient (too big) spanning sets for a vector space V . For example {(1, 0), (0, 1), (1, 1)} is a spanning set for R 2 but any two of the three vectors still spans. Dependence Relation Let v1, v2, . . . , vn ∈ V . Then a dependence relation between v1, v2, . . . , vn is an equation c1v1 + c2v2 + . . . + cnvn = 0, c1, c2, . . . cn ∈ R. The dependence relation is said to the trivial dependence relation if all the c 0 i s are zero. So in the above 1•(1, 0) + 1•(0, 1) − 1•(1, 1) = 0. is a dependence relation