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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 fourthorder diﬀerential equation
x + 6x − 3x + x = cos 3t into an equivalent system of ﬁrstorder diﬀerential equations. Write your
system in matrix form.
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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.
 Fall '08
 Zhang

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