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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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 65E
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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
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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