Note that the real row vectors also form a vector space over R; and they are essentially the same as the column vectors as far as vector spaces are concerned.For convenience,we may also consider R"as a row vector space if no confusion is caused.However,in the matrix-vector product Ax,obviously r needs to be a column vector. Let S be a nonempty subset of a vector space V over a field F. Denote by Span S the collection of all finite linear combinations of the vectors in S;that is,Span S consists of all vectors of the form C1v1+C22+…+Ctt,t=1,2,,c∈F,吃∈S, The set Span S is also a vector space over F.If Span S=V,then every vector in V can be expressed as a linear combination of vectors in S.In such cases we say that the set S spans the vector space V. A set S={v1,v2,...,vk}is said to be linearly independent if C1U1+C2U2+·+CkVk=0 holds only when ci =c2=...=ck=0.If there are also nontrivial solutions,i.e.,not all c are zero,then S is linearly dependent. 55