Let [tex]V\subset\,R^n[/tex] be a subpace with [tex]dim(V) = D[/tex]. Prove that any [tex]S[/tex] vectors in [tex]V[/tex] are linearly dependent if [tex]S > D[/tex].
The Attempt at a Solution
[tex]dim(V) = D[/tex] implies that there are [tex]D[/tex] vectors in a basis for [tex]V[/tex]. If [tex]S > D[/tex] then there will be at least one more vector in the set, which will result in a free variable and thus, infinite solutions; implying that the set will be linearly dependent.