Q2. Consider the homogeneous CLTI system i = Ax. The characteristic equation of A is given by: det(A – Al) = (1 – 14)(1 – 2)²(2 – A3)³, where l4 are the eigenvalues of A. Also, it is given that dim N(A – A21) = 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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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