HW6 - EEL3105 Fall2011 Homework6 Note: met....

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EEL 3105 Fall 2011 Homework 6 Note: Problem 4 will be graded separately for assessing that one of the course objectives is met. Please submit solution to Problem 4 as a separate document. Consider matrices 1 2 1 2 3 1 3 4 0 1 0 1 0 0 0 1 A k B b b C c c c 1. For A, choose k = 3. Find the eigenvalues of the resulting matrix. Are they real? Why? 2. Find a formula for eigenvalues of A as a function of k. Suppose k is a design parameter which ranges from 100 to +100. Use the formula to plot the eigenvalues of A as a function of k in the complex plane. Use MATLAB to verify your answer. Such a plot is called root locus. Comment on your results. 3. Find characteristic polynomials of B and C in terms of b 1 , b 2 , c 1 , c 2 , and c 2 . Do you see any pattern in your answer? Can you think of a way to generalize this to an nxn matrix?

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