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1.Let f t 2P jf(0) = f(1)g. Show that is a subspace of and ...
euclid.colorado.edu1.Let V = ff(t) 2P 3jf(0) = f(1)g. Show that V is a subspace of P 3 and nd a basis of V. The neutral element of P 3 is the function n(t) = 0. In particular, n(0) = 0 = n(1), so n(t) 2V. ... Show that V is a subspace of R 3 and nd a basis of V. The neutral element is the 3 T3 zero matrix 0. Clearly 0 = 0, so 0 …
Solutions to Homework 11 - University of Texas at Austin
web.ma.utexas.edua subspace of Rn? Solution: Assume that W = n ~x A~x =~b o is a subspace of Rn. Then, if ~x 0 is in W, so is 2~x 0. Since ~x 0 is in W, we have that A~x 0 =~b This means that A(2~x 0) = 2A~x 0 = 2~b But for 2~x 0 to be in W, we must by de nition have A(2~x 0) = ~b. Therefore, we must have that ~b = 2~b which implies that our only possibility is ...