Linear Algebra: Vector Space proof.... I'm really having trouble comprehending this problem. This is not exactly a "homework problem" but I need a good, formal definition of this to help with some other problems. Let (Vectors) V1, V2,......,Vk be vectors in vector space V. Then the set W of all linear combinations of Vectors V1, V2,.....Vk is a "subspace" of V. Exactly how do you prove this? After setting up two vectors to find the subspace, I'm lost. Gladly appreciate any help.