Consider two finite dimensional (real) vector spaces V and W with dim(V) = n and dim(W) : k. Define (V, W) to be the set of linear transformations: (V, W) : {T : The map T: V > W is linear} 1. Define addition and scaling on E(V, W) 2. Sketch a proof that 130/, W) is a vector space. 3. Prove that (V, W) is finite dimensional by finding an explicit basis for it