2. If possible , daonalize the matrex A = explain why. [引1 If this is not possible,
2. If possible , daonalize the matrex A = explain why. [引1 If this is not possible,
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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The eigenvalue should be 2-2i, which with 8 would create a 1/4 ratio. Also, the row [1 0] is the first, not second row as I have it. I'm not sure at which step I've made a mistake. Any help would be appreciated
![2. If possible, diagonalıze the matrix A=
explain why.
i. If this is mot possible,
det ( A - AZ) = | 4-Xz
1
-2
- (4-X1)(1-x) +2 =0
x²-S^+6=0
(A3 )(^-2) = 0 , x:3,2
1-XI
(A-XI )x = 0, d=2
A= Pppt, D=řAP
D=PAP
ady P
det e
P=
-1 1
-2
-2
& free
1-2 1 1
-1 2
4-2
1.
1 -1
=-4+2 2+4
4+1 2-1
-2 +6 4+
1 1
14 27
I+S
1e +1
11
1 -1
-1 2
1
-1
2-1
D- G i]-网
4-1 -21-
-4+2
3 -3
1 1
11
2+2
6-3 3-3
L-4+4 -244
3 0
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb01156c3-4f42-4f24-8d9e-b5123e3d8863%2Ffb4f45a0-5d0e-43a6-a702-85d40641290b%2Fqlac7t_processed.png&w=3840&q=75)
Transcribed Image Text:2. If possible, diagonalıze the matrix A=
explain why.
i. If this is mot possible,
det ( A - AZ) = | 4-Xz
1
-2
- (4-X1)(1-x) +2 =0
x²-S^+6=0
(A3 )(^-2) = 0 , x:3,2
1-XI
(A-XI )x = 0, d=2
A= Pppt, D=řAP
D=PAP
ady P
det e
P=
-1 1
-2
-2
& free
1-2 1 1
-1 2
4-2
1.
1 -1
=-4+2 2+4
4+1 2-1
-2 +6 4+
1 1
14 27
I+S
1e +1
11
1 -1
-1 2
1
-1
2-1
D- G i]-网
4-1 -21-
-4+2
3 -3
1 1
11
2+2
6-3 3-3
L-4+4 -244
3 0
2
Transcribed Image Text:(A -(2-21)エ)文-る
-8 2+2;• |3R -3
242:, R,-(2-)R1
-2+1
1
-8 24 21
-24i 1
1(-241) 30
(23)(22)こ4-21+2: -4? = 8
-8xx= (-2-2: )Xz
メx frae
-8 2+2 0
又=
4
B=
X2
1
1
x(金)。
Cこ
入: 2-2:
入= a -61
a:2
1
6=2
Cニ
P=
2 2
1
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