2. Given the following matrix A, 9 -6 3 -7 14 -10 6 -14 24 -18 11-24 8 -6 3 -6 Find matrices D and P such that A = D= P= PDKP-1 1 2 31 1 2 2 1 3226 2 32 P"= 2 2 -7 4 14 -8 -1 5 -3 2 -15

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Although the answers are provided, I'm still confused about how to solve for D and P. Any help would be greatly appreciated, and thanks in advance.

2. Given the following matrix A,
9
14
24
8
D=
-6 3 -7
-10
6 -14
-18
11
-24
-6 3
-6
-1
Find matrices D and P such that A* = PD"P
okp²¹.
k
P=
3 1
1
1 2
2
1
3226
32
12
2
P".
14
-8
-1
5
-3
2
-7
4
OC
2
-15
9
1
Transcribed Image Text:2. Given the following matrix A, 9 14 24 8 D= -6 3 -7 -10 6 -14 -18 11 -24 -6 3 -6 -1 Find matrices D and P such that A* = PD"P okp²¹. k P= 3 1 1 1 2 2 1 3226 32 12 2 P". 14 -8 -1 5 -3 2 -7 4 OC 2 -15 9 1
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In Step 2 (Description of the steps), I see that you're finding the eigen values of matrix A. I see that you set A - (lambda)i = 0. Next you say "Solving this, we get

(lambda2-1) (lambda-2)2 = 0 ---> lambda = 1, -1, 2, 2". Can you please explain how solved to get the "(lambda2-1) (lambda-2)2 = 0 ---> lambda = 1, -1, 2, 2" ?

I thought that I was supposed to find the characteristic polynomials (the values from the diagonals - in this case, 9-lambda, -10-lambda, etc.), set them equal to zero (9-lambda=0, -10-lambda=0, etc.) solve for the lambda values (lambda=9, lambda=-10, etc.), and use those lambda values in the D matrix. 

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