1 0 07 Let A = 0 0 2 0 3 0 %3D Find the Characteristic Polynomial, and compute the Eigenvalues: O p(X) = X3 – 6X² + 11A – 6 = A1 = 1, d2 = 2, X3 = 3 O-p(X) = X – 2A2 – 5X + 6= A1 = 1, X2 = -2, A3 = 3 O-p(X) = X3 +7A + 6 = A1 = 1, d2 = 2, X3 = -3 O-p(X) = X3 4X² + 1A – 6 → A1 = 1, A2 = -2, A3 = -3 O-p(X) = X³ – X² – 6X + 6 > A1 = 1, d2 = v6, A3 = -V6 O-p(A) = X3 –X2 – 3A + 3= A1 = 1, X2 = v3, A3 = -V3 O-p(A) = X3 – X² – 2A + 2 → d1 = 1, X2 = /2, d3 = -/2 %3D - %3D %3D %3D %3D %3D %3D %3D %3D %3D %3D %3D
1 0 07 Let A = 0 0 2 0 3 0 %3D Find the Characteristic Polynomial, and compute the Eigenvalues: O p(X) = X3 – 6X² + 11A – 6 = A1 = 1, d2 = 2, X3 = 3 O-p(X) = X – 2A2 – 5X + 6= A1 = 1, X2 = -2, A3 = 3 O-p(X) = X3 +7A + 6 = A1 = 1, d2 = 2, X3 = -3 O-p(X) = X3 4X² + 1A – 6 → A1 = 1, A2 = -2, A3 = -3 O-p(X) = X³ – X² – 6X + 6 > A1 = 1, d2 = v6, A3 = -V6 O-p(A) = X3 –X2 – 3A + 3= A1 = 1, X2 = v3, A3 = -V3 O-p(A) = X3 – X² – 2A + 2 → d1 = 1, X2 = /2, d3 = -/2 %3D - %3D %3D %3D %3D %3D %3D %3D %3D %3D %3D %3D
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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Transcribed Image Text:1 0 07
0 0 2
0 3 0
Let A =
%3D
Find the Characteristic Polynomial, and compute the Eigenvalues:
O-p(X) = X3 – 6X² + 11A – 6 = A1 = 1, d2 = 2, X3 = 3
O-p(X) = X3 – 2A2 – 5X + 6= A1 = 1, X2 = -2, A3 = 3
O -p(A) = X3 + 7A + 6 = X1 = 1, d2 = 2, A3 = -3
O -p(A) = X³ 4X² + 1A – 6 → A1 = 1, A2 = -2, A3 = -3
O-p(A) = X3 – X? – 6X + 6 → A, = 1, A2 = v6, Ag =-V6
O-p(X) = X³ – X² – 31 + 3 → A, = 1, A2 = v3, dg = -V3
O-p(A) = X3 – X² – 21 + 2 → d1 = 1, A2 = /2, d3 = -/2
000
Transcribed Image Text:Let A =
Find the Characteristic Polynomial, and compute the Eigenvalues:
They are (note i = v-1) is the iaginary "unit"):
O p(A) = X² + 21 +1=A1 = -1, and A2 = -1,
O p(A) = X² – 1=\1 = -1, and A2 = 1
O p(A) = X² – A +1=A1 = 1, and dz
O p(A) = X² + 2A + 2 = A1 = -1+ i, and X2 = -1 - i
O p(A) = X – 2A + 2 A1 = 1 + i, and A, = 1 – i
O p(A) = X2 +1=\1 = i, and A2 = -i
1
W
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000 F4
F3
E5
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