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Question

Suppose U 1 ,...,U m are subspaces of V. The sum of U 1 ,...,U m ,When dealing with vector spaces, we are usually interested only in subspaces, as opposed to arbitrary subsets. The union of subspaces is rarely a subspace (see Exercise 9 in this chapter), which is why we usually work with sums rather than unions. denoted U 1 +···+U m , is deﬁned to be the set of all possible sums of elements of U 1 ,...,U m

Answer

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Question

Suppose U 1 ,...,U m are subspaces of V. The sum of U 1 ,...,U m ,When dealing with vector spaces, we are usually interested only in subspaces, as opposed to arbitrary subsets. The union of subspaces is rarely a subspace (see Exercise 9 in this chapter), which is why we usually work with sums rather than unions. denoted U 1 +···+U m , is deﬁned to be the set of all possible sums of elements of U 1 ,...,U m

Answer

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Question

Suppose U 1 ,...,U m are subspaces of V. The sum of U 1 ,...,U m ,When dealing with vector spaces, we are usually interested only in subspaces, as opposed to arbitrary subsets. The union of subspaces is rarely a subspace (see Exercise 9 in this chapter), which is why we usually work with sums rather than unions. denoted U 1 +···+U m , is deﬁned to be the set of all possible sums of elements of U 1 ,...,U m

Answer

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