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Let A = %3D Find the Characteristic Polynomial, and compute the Eigenvalues: They are (note i = v-1) is the iaginary "unit"): O p(A) = X + 2X +1=A1 = -1, and A2 = -1, %3D O p(A) = X² - 1=\1 = -1, and d2 = 1 O p(X) = X² – 21 +1= A1 = 1, and A2 = 1 %3D %3D %3D %3D O p(X) = X² + 2X + 2= A1 =-1+i,and = -1-i %3D %3D O p(A) = X2 - 2A + 2=A1 = 1+ i, and A2 = 1 - i O p(A) = X2 + 1=1 = i, and A2 = -i %3D %3D

Let A = %3D Find the Characteristic Polynomial, and compute the Eigenvalues: They are (note i = v-1) is the iaginary "unit"): O p(A) = X + 2X +1=A1 = -1, and A2 = -1, %3D O p(A) = X² - 1=\1 = -1, and d2 = 1 O p(X) = X² – 21 +1= A1 = 1, and A2 = 1 %3D %3D %3D %3D O p(X) = X² + 2X + 2= A1 =-1+i,and = -1-i %3D %3D O p(A) = X2 - 2A + 2=A1 = 1+ i, and A2 = 1 - i O p(A) = X2 + 1=1 = i, and A2 = -i %3D %3D

Advanced Engineering Mathematics
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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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= X1 = -1, and A2 = -1, O p(A) = X2 - 1=A1 = -1, and d2 = 1 O p(A) = X² – 21 +1= A1 = 1, and A2 = 1 O (A) = X² + 21 + 2 = A1 = -1+ i, and Ag = -1 – i O p(X) = X2 - 2A + 2 A1 = 1+i, and A2 = 1 - i O p(A) = X2 +1=\1 = i, and d2 = -i DEC
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= X1 = -1, and A2 = -1, O p(A) = X2 - 1=A1 = -1, and d2 = 1 O p(A) = X² – 21 +1= A1 = 1, and A2 = 1 O (A) = X² + 21 + 2 = A1 = -1+ i, and Ag = -1 – i O p(X) = X2 - 2A + 2 A1 = 1+i, and A2 = 1 - i O p(A) = X2 +1=\1 = i, and d2 = -i DEC
0 1 Let A = %3D 1 0 Find the Characteristic Polynomial, and compute the Eigenvalues: They are (note i = v-1) is the imaginary "unit"): O p(X) = X2 + 21 +1=Xj = -1, and A, = -1, O p(X) = X² – 1=X1 = -1, and A2 = 1 O p(A) = X² – 24 +1=\1 = 1, and A2 = 1 O p(A) = X +2A +2= A1 = -1+ i, and A2 = -1 - i O p(A) = X2 - 2A + 2 A1 = 1+ i, and A2 = 1 - i O p(A) = X2 +1=X1 = i, and A2 = -i %3D %3D DEC 000 D00 F4 F3 F5 F6 F7
Transcribed Image Text:0 1 Let A = %3D 1 0 Find the Characteristic Polynomial, and compute the Eigenvalues: They are (note i = v-1) is the imaginary "unit"): O p(X) = X2 + 21 +1=Xj = -1, and A, = -1, O p(X) = X² – 1=X1 = -1, and A2 = 1 O p(A) = X² – 24 +1=\1 = 1, and A2 = 1 O p(A) = X +2A +2= A1 = -1+ i, and A2 = -1 - i O p(A) = X2 - 2A + 2 A1 = 1+ i, and A2 = 1 - i O p(A) = X2 +1=X1 = i, and A2 = -i %3D %3D DEC 000 D00 F4 F3 F5 F6 F7
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