(1) Let U and W be two subspaces of a vector space of V. Prove that the set U+ W= {v|v=u+w, where u EU and we W} is a su

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1 Let U And W Be Two Subspaces Of A Vector Space Of V Prove That The Set U W V V U W Where U Eu And We W Is A Su 1 (27.84 KiB) Viewed 55 times

(1) Let U and W be two subspaces of a vector space of V. Prove that the set U+ W= {v|v=u+w, where u EU and we W} is a subspace of V. (2) Let U and W be two subspaces of a vector space of V=R³. U= {(x,y,x-y) | x, y≤ R} W= {(a,0,x) | ER} X= {(x,x,x) | x≤ R} Find a basis of U, W, X and U+ W, U+ X, and W+X.