Problem 2: The second order equation d 2 y dt 2 + 2 dy dt +...

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Math 286 B1/D1 Midterm Exam 3 April 20, 2017 Solutions: Test Form A Test Section 1: Multiple Choice Problems Problem 1: What is the characteristic polynomial of the following matrix? A = 2 1 1 3 (a) λ 2 + 6 λ + 5 (b) λ 2 - 6 λ + 5 (c) λ 2 - 6 λ + 7 (d) λ 2 + 5 λ - 5 (e) λ 2 - 5 λ + 5 Problem 2: The second order equation d 2 y dt 2 + 2 dy dt + 5 y = 0 is equivalent to which of the following first order system of equations? (a) d dt y p = 0 5 1 2 y p (b) d dt y p = 0 5 - 1 - 2 y p (c) d dt y p = 0 1 - 5 2 y p (d) d dt y p = 0 1 - 5 - 2 y p (e) d dt y p = 0 1 5 2 y p
Problem 3: True or False: An n × n matrix A always has exactly n linearly independent eigenvectors.
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Problem 4: What is the best way to express the system of differential equations dx dt = 5 x + 3 y dy dt = 2 x + 7 y in matrix form?
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