Please correct the solution, there is an error in the solution Example: Fined all eigen values and eigen vectors of the matrix and check that P'AP is diagonal matrix 8. -8 8 A = 9 -15 - 18 = P(1) = det(A– A1)= 0= -5 11 14 8 -8 8 [a 0 9 - 15 - 18 -|0 0=0= 2 - 7a² +121 = 0 - 5 11 14 = 2(2 – 72 +12) = 0= 1(2– 4)(2 – 3)= 0 ..4 = 4 ,2, = 3 ,Az = 0 CASE : 2, = 4 =(A-41)X, = 0 8. -8 8. -15 -18 X2 = X, =|0 Similarly - 5 11 14 X2 ; X3 = 3 .. we can construct the matrix P 2 1 P = [x,: X,: x,]=|0 1 1 - 2 -1 2 0 0 p-l = 3 -5 - 6 ,P-'AP =| 0 3 0 1 -1 -1 0 0 4
Please correct the solution, there is an error in the solution Example: Fined all eigen values and eigen vectors of the matrix and check that P'AP is diagonal matrix 8. -8 8 A = 9 -15 - 18 = P(1) = det(A– A1)= 0= -5 11 14 8 -8 8 [a 0 9 - 15 - 18 -|0 0=0= 2 - 7a² +121 = 0 - 5 11 14 = 2(2 – 72 +12) = 0= 1(2– 4)(2 – 3)= 0 ..4 = 4 ,2, = 3 ,Az = 0 CASE : 2, = 4 =(A-41)X, = 0 8. -8 8. -15 -18 X2 = X, =|0 Similarly - 5 11 14 X2 ; X3 = 3 .. we can construct the matrix P 2 1 P = [x,: X,: x,]=|0 1 1 - 2 -1 2 0 0 p-l = 3 -5 - 6 ,P-'AP =| 0 3 0 1 -1 -1 0 0 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Please correct the solution, there is an
error in the solution
Example: Fined all eigen values and eigen vectors of the matrix and
check that P'AP is diagonal matrix
8.
-8
8
A =
-15
-18
» P(2) = det(A– AI) = 0=
-5
11
14
8.
- 8
8
- 15 - 18
0=0= 2 - 72 +122 = 0
-5
11
14
= 1(2' – 72 +12)= 0= 1(2– 4)(2 – 3) = 0
..4 = 4 ,1, = 3 ,Az = 0
CASE : 2, = 4 =(4-4I)X, = 0
8.
-8
8.
9.
-15
-18
= X, =|0
Similarly
-5
11
14
X3
X, =|1
; X3 =
3
.. we can construct the matrix P
1
[2 0
1
P= [X,: X,: x,]=|0
1
3
1
-1
2
0 0
P- = 3
-5
- 6
,P-AP =| 0 30
1
-1
-1
0 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11005a7a-c188-44e8-af66-5e34ca41fb3b%2F9b4ffdd7-f16c-46fe-8096-61162fd210c6%2Fy6y28mg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Please correct the solution, there is an
error in the solution
Example: Fined all eigen values and eigen vectors of the matrix and
check that P'AP is diagonal matrix
8.
-8
8
A =
-15
-18
» P(2) = det(A– AI) = 0=
-5
11
14
8.
- 8
8
- 15 - 18
0=0= 2 - 72 +122 = 0
-5
11
14
= 1(2' – 72 +12)= 0= 1(2– 4)(2 – 3) = 0
..4 = 4 ,1, = 3 ,Az = 0
CASE : 2, = 4 =(4-4I)X, = 0
8.
-8
8.
9.
-15
-18
= X, =|0
Similarly
-5
11
14
X3
X, =|1
; X3 =
3
.. we can construct the matrix P
1
[2 0
1
P= [X,: X,: x,]=|0
1
3
1
-1
2
0 0
P- = 3
-5
- 6
,P-AP =| 0 30
1
-1
-1
0 4
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