(a) Prove that H + K is a subspace of V. (b) Let {V₁,..., Vn} be a basis of H and {u₁,..., um} be a basis of K. Show that H + K = span{V₁, V, U₁₁, Um}. H+K={v+u\v € H₂u€ K}. Here are some ways to show two sets A and B are equal: • Show ACB and BCA; or Show that w € A if and only if w€ B. (c) Consider subspaces of Rª H = span 000 000) Find a basis for the subspace H + K of V. and determine the dimension of H+K. and K = span

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