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Q2. Consider the homogeneous CLTI system i = Ax. The characteristic equation of A is given by: det(A – Al) = (A – 14)(1 – 2)²(2 – 13)', where l4 are the eigenvalues of A. Also, it is given that dim N(A – 121) = dim N(A – A31) = 2, where N(.) denotes the nullity of the operand. Find all possible Jordan canonical forms for A. Explain your answer.

Q2. Consider the homogeneous CLTI system i = Ax. The characteristic equation of A is given by: det(A – Al) = (A – 14)(1 – 2)²(2 – 13)', where l4 are the eigenvalues of A. Also, it is given that dim N(A – 121) = dim N(A – A31) = 2, where N(.) denotes the nullity of the operand. Find all possible Jordan canonical forms for A. Explain your answer.

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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Consider the homogeneous CLTI system. The characteristic equation of A given by: det(A-λ*I)=(λ-λ1)(λ-λ2)^2(λ-λ3)^3,

where λi are the eigenvalues of A. Also, it is given that 

dimN(A-λ2*I)=dimN(A-λ3*I)=2 where N(.) denotes the nullity of operand. Find all possible Jordan canonical forms for A. Explain your answer. 

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Q2. Consider the homogeneous CLTI system i = Ax. The characteristic equation of A is given by: det(A – A1) = (1 – 14)(1 – 2)²(1 – A3)³, where l4 are the eigenvalues of A. Also, it is given that dim N(A – 121) = dim N(A – A31) = 2, where N(.) denotes the nullity of the operand. Find all possible Jordan canonical forms for A. Explain your answer.
Transcribed Image Text:Q2. Consider the homogeneous CLTI system i = Ax. The characteristic equation of A is given by: det(A – A1) = (1 – 14)(1 – 2)²(1 – A3)³, where l4 are the eigenvalues of A. Also, it is given that dim N(A – 121) = dim N(A – A31) = 2, where N(.) denotes the nullity of the operand. Find all possible Jordan canonical forms for A. Explain your answer.
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