Final10 - MA366 Make-up Final Last Name: First Name: Show...

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MA366 Make-up Final Last Name: First Name: Show all work. A correct answer without supporting work is worth NO credit! (Some calculators can solve diﬀerential equations.) There should be no “hard” integrals, unless you mess up somewhere. If this happens, just leave it as an integral and explain how to ﬁnish the problem. 1

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2 (1) The following vectors X 1 and Y 1 are eigenvectors for a certain 3 × 3 matrix A corresponding to the eigenvalues 3 and 1 + 2 i respectively. Find the general solution to the system X 0 = AX in real form . No complex numbers allowed! 5 pts. X 1 = 0 3 1 , Y 1 = i - 1 i - 2 .
3 (2) Given that X 1 , X 2 and X 3 are eigenvectors for the following matrix, ﬁnd the general solution to X 0 = AX . Hint: To ﬁnd the eigenvalue, compute AX i . 5 pts. A = - 3 6 - 3 4 - 3 2 6 - 12 6 X 1 = 1 0 - 2 X 2 = - 1 1 2 X 3 = - 1 2 5

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4 (3) The characteristic polynomial for the following matrix is p ( r
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This note was uploaded on 04/25/2011 for the course MA 366 taught by Professor Cho during the Spring '08 term at Purdue University-West Lafayette.

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Final10 - MA366 Make-up Final Last Name: First Name: Show...

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