MATH 272 Final: MATH 272 Amherst S12m272Final
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: [15 points] consider the following matrix a and vector b: Justify your answers: [15 points] consider the matrix where is a xed scalar. 0 0 2 (a) assume that 6= 0. Prove that a is not diagonalizable. (b) for the rest of the problem, we will assume that = 0. Find an invertible matrix p such that p 1ap is diagonal. (c) still assuming = 0, give a formula for ak, where k is a positive integer. 2: [9 points] answer the following with a brief explanation: (a) suppose a is a 5 7 matrix. If the general solution to the homogeneous system. Assume that over each one-year period wmkc captures 10% of wlin"s market share and wlin captures 20% of wmkc"s market share.
