Given subspaces H and K of a vector space V, the sum of H and K, written as H + K, is the set of all vectors in V that can be written as the sum of two vectors, one in H and the other in K; that is,
H + K = {w : w = u + v for some u in H and some v in K }
a. Show that H + K is a subspace of V.
b. Show that H is a subspace of H + K and K is a subspace of H+ K.
I am completely lost on this problem so any information on a solution or how to solve it would be greatly appreciate. Thanks a lot.
2007-10-24
08:53:20
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3 answers
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asked by
swierczawack
2