We are doing vector spaces in my math class right now and I'm TOTALLY lost. Here are a few of the problems I don't get:
Let u and v be (fixed) vectors in the vector space V. Show that the set W of all linear combinations ab+bv of u and v is a subspace of V.
Prove: If the (finite) set S of vectors contains the zero vector, then S is linearly dependent.
Determine whether or not the given vectors in Rn form a basis for Rn.
v1=(3,-7,5,2), v2=(1,-1,3,4), v3=(7,11,3,13)
Let {v1,v2,...,vk} be the basis for the proper subspace W of the vector space V, and suppose that the vector v of V is not in W. Show that the vectors v1,v2,...,vk,v are linearly independent.
Please help! Thanks!