# another linear algebra question I can't get

• January 19th 2008, 04:12 PM
alexmin
another linear algebra question I can't get
suppose that V is finite dimensional, with dimV=n. Prove that there exist one-dimensional subspaces U1,...,Un (1 and n are supposed to be subscripts)of V such that

V = U1 + ... + Un (again, 1 and n are subscripts and + denotes a direct sum)
• January 19th 2008, 04:34 PM
ThePerfectHacker
Quote:

Originally Posted by alexmin
suppose that V is finite dimensional, with dimV=n. Prove that there exist one-dimensional subspaces U1,...,Un (1 and n are supposed to be subscripts)of V such that

V = U1 + ... + Un (again, 1 and n are subscripts and + denotes a direct sum)

If $\mbox{dim}(V) = n$ it means it has a basis $\bold{v}_1,...,\bold{v}_n$. Let $U_i = \mbox{span}(\bold{v}_i)$ then $U_1+...+U_n = V$.