Tuesday, 31 May 2005Name:Math 5A, Final Exam Review1. LetA=105216014.a. Compute detA.b. ComputeA-1. Verify that this is, indeed, the inverse ofA.c. SolveAx=b, whereb=567.2. Suppose for a mass-spring system, one obtains the differential equationx+ 4x+ 5x= 0, with initial valuesx(0) = 1 andx(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. Solvey-4y= 6e2t.b. Write the aforementioned differential equation as an equivalent system of firstorder differential equations.
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