341hw11 - Homework 11, due Friday November 18th, in class...

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Unformatted text preview: Homework 11, due Friday November 18th, in class 1. For each of the following, find an invertible matrix X and a diagonal matrix D such that A = XDX −1 . In other words, diagonalize the matrix A. 1a. A= 1b. 5 6 −2 −2 100 A = −2 1 3 1 1 −1 1c. 1 2 −1 A = 2 4 −2 3 6 −3 2. For each of the matrices in Question 1, compute A5 . 3. For each of the matrices in Question 1, compute eA . 44 be diagonalized? Why or why not? −1 0 22 3 6 be diagonalized? Why or why not? 5. Can the matrix A = 0 5 0 −2 −2 4. Can the matrix A = 6. Let A be the matrix −3 −6 0 2 4 0 . 0 02 With the help of diagonalization, find a general expression for Ak . 7. Transform the fourth-order differential equation x + 6x − 3x + x = cos 3t into an equivalent system of first-order differential equations. Write your system in matrix form. 1 ...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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