Consider the vectors v1dot v2dotvmdot Rn Is spanvldot vmdot

Consider the vectors v_1dot, v_2dot,...v_mdot R^n. Is span(v_ldot, v_mdot) necessarily a subspace of R^n? Justify your answer.

Solution

Given that the m vectors span R^n

By definition this means span {v1 v2...vm} is the intersection W of all subspaces of R^n that contain

S

By theorem 1, The subspace spanned by a non-empty subset S of a vector space V is the set of all linear combinations of vectors in S.

Hence the span is a vector space.