MATH 272 Final: MATH 272 Amherst S13M272 28Leise 29Final
15 Feb 2019
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You may not use any calculators or other devices or any notes. Explain answers clearly and completely and show all work in your blue book. Please turn o all devices including cell phones. The total number of points is 100: [15 points] consider the following matrix a and vector b: [15 points] let h , i be an inner product on a vector space v and let w v be a subspace. Recall that the orthogonal complement of w in v is. W = {v v | hv, wi = 0 for all w w }. (a) prove that w is a subspace of v . (b) suppose that w = span{w1, . X = {v v | hv, w1i = hv, w2i = = hv, wni = 0}. Prove that w = x. (c) let v = r3 and w =( . Find a basis for w : [10 points] consider the matrix a =" 1.
