Math 110: Worksheet 1 Solutions
i by setting t = 0 in the de nitions. let x;y 2W i. There then exist t;s 2R such that x = tv i and y = sv i so that x+ y = tv i + sv i = (t+ s)v i 2W i: 6 let x 2W i and a 2R. Note then that ax = a(tv i) = (at)v i 2W i: We conclude that both W 1 and W 2 are subspaces of V. (b) Show that V = W 1 W 2. We need to show that (i) W 1 \W 2 = f0gand ...
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