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Question: for a field k show that the following are subspaces...

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For a field K show that the following are subspaces of Kn:

TL. 1.4 (Subspaces) For a field K show that the following are subspaces of K PTL a) Var-(xi,...,xn) K(i-1,..., n); TTL (2+2 P.) 1.5 (Union of subspaces) Let U1, U2 subspaces of the vector space V. Show that (4 P.) U1 UU2 is a subspace (of V) if and only if Ui C U2 or U2 C U.

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