Suppose U1;:::;Um are finite-dimensional subspaces of V such thatU1 C C Um is a direct
Chapter 2, Problem 16(choose chapter or problem)
Suppose U1;:::;Um are finite-dimensional subspaces of V such thatU1 C C Um is a direct sum. Prove that U1 Um is finitedimensionalanddim U1 Um D dim U1 CC dim Um:[The exercise above deepens the analogy between direct sums of subspacesand disjoint unions of subsets. Specifically, compare this exerciseto the following obvious statement: if a set is written as a disjoint unionof finite subsets, then the number of elements in the set equals the sum ofthe numbers of elements in the disjoint subsets.]
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