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Show that V=W W for the given vector space V and the given subspaces W and W. (a) V = R, W = {(x,

Show that V=W W for the given vector space V and the given subspaces W and W. (a) V = R, W = {(x, x2, x3): x + x + x3 = 0}, W = {(0, 0, x3): x3 = R}. (b) V = M33 (C), W = {A: Ajj = 0 for i > j}, W = {A: Aj = 0 for i j}. (c) V = P (R), W = {f(x): f(x) = f(-x)}, W = {f(x): f(-x) = -f(x)}.

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