Recall for subspaces U,V of R",U + V = {u+v: u € U, v e V}. This is a subspace of R" referred to as the sum of U and V. In this problem you are asked to prove that dim(U + V) = dim(U)+ dim(V) – dim(U...

Extracted text: Recall for subspaces U,V of R",U + V = {u+v: u € U, v e V}. This is a subspace of R" referred to as the sum of U and V. In this problem you are asked to prove that dim(U + V) = dim(U)+ dim(V) – dim(U n V). Hint: You need to show that U + Ww has a basis with size dim(U) + dim(W) – dim(U n W). Recall a basis is of a subspace X of R" is a sequence of vectors from X which is linearly independent and spans X.