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05fp - Tuesday 31 May 2005 Name Math 5A Final Exam Review...

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Tuesday, 31 May 2005 Name: Math 5A, Final Exam Review 1. Let A = 1 0 5 2 1 6 0 1 4 . a. Compute det A . b. Compute A - 1 . Verify that this is, indeed, the inverse of A . c. Solve Ax = b , where b = 5 6 7 . 2. Suppose for a mass-spring system, one obtains the differential equation x + 4 x + 5 x = 0, with initial values x (0) = 1 and x (0) = 0. a. Solve the equation. Write it in its phase-amplitude form. b. What is the earliest time at which this system crosses its equilibrium position? 3. a. Solve y - 4 y = 6 e 2 t . b. Write the aforementioned differential equation as an equivalent system of first order differential equations.
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