MATH 280 Final: MATH 280 Amherst S16M280Final
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: [20 points] consider the following matrix a and vector b: If so, express as a linear combination of the basis vectors you found in part (c): [10 points] let w = span( . Find an orthonormal basis for w : [10 points] prove that the null spaces of a and ata are identical for any m n matrix. A: [10 points] consider the matrix a =" 1. 1 (a) find the eigenvalues and eigenvectors of a. (b) find an invertible matrix p such that d = p 1ap is diagonal. Note that since a is symmetric, you can choose p to be an orthogonal matrix. (c) determine a formula for ak.
