The characteristic equation of the coefficient matrix A of the system -8 -3 -18 -1 -9 -3 -25 х -9 33 10 90 32 is $(1) = (1² – 42 + 13)² = 0. Therefore, A has the repeated complex conjugate pair 2 + 3i of eigenvalues. First show that the complex vec- tors V1 = [ -i 3+ 3i 0 -11". v2 = [3 -10 + 9i o]" -i form a length 2 chain {v1, v2} associated with the eigen- value A = 2+ 3i. Then calculate (as in Problem 33) four independent real-valued solutions of x' = Ax.
The characteristic equation of the coefficient matrix A of the system -8 -3 -18 -1 -9 -3 -25 х -9 33 10 90 32 is $(1) = (1² – 42 + 13)² = 0. Therefore, A has the repeated complex conjugate pair 2 + 3i of eigenvalues. First show that the complex vec- tors V1 = [ -i 3+ 3i 0 -11". v2 = [3 -10 + 9i o]" -i form a length 2 chain {v1, v2} associated with the eigen- value A = 2+ 3i. Then calculate (as in Problem 33) four independent real-valued solutions of x' = Ax.
Transcribed Image Text:The characteristic equation of the coefficient matrix A of
the system
-8
-3
-18
-1
-9
-3
-25
х
-9
33
10
90
32
is
$(1) = (1² – 42 + 13)² = 0.
Therefore, A has the repeated complex conjugate pair
2 + 3i of eigenvalues. First show that the complex vec-
tors
V1 = [ -i
3+ 3i
0 -11".
v2 = [3 -10 + 9i
o]"
-i
form a length 2 chain {v1, v2} associated with the eigen-
value A = 2+ 3i. Then calculate (as in Problem 33) four
independent real-valued solutions of x' = Ax.
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![The characteristic equation of the coefficient matrix A of
the system
-8
-3
-18
-1
-9
-3
-25
х
-9
33
10
90
32
is
$(1) = (1² – 42 + 13)² = 0.
Therefore, A has the repeated complex conjugate pair
2 + 3i of eigenvalues. First show that the complex vec-
tors
V1 = [ -i
3+ 3i
0 -11".
v2 = [3 -10 + 9i
o]"
-i
form a length 2 chain {v1, v2} associated with the eigen-
value A = 2+ 3i. Then calculate (as in Problem 33) four
independent real-valued solutions of x' = Ax.](https://content.bartleby.com/qna-images/question/728a8dfa-1614-4c2d-888e-a56a40365397/59826f6a-2026-476b-ba61-6b5ec9a699ce/c1g7fjc.png)
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