Consider the homogeneous CLTI system ?̇ = ??. The characteristic equation of ? is given by:det(? − ??) = (? − ?3)(? − ?4)4(? − ?5)5,where ?7 are the eigenvalues of ?. Also, it is given thatdim?(? − ?4?) = dim?(? − ?5?) = 2,where ?(. ) denotes the nullity of the operand. Find all possible Jordan canonical forms for ?. Explainyour answer. Q2. Consider the homogeneous CLTI system x= Ax. The characteristic equation of A is given by:det(A – A1) = (1 – 14)(1 – 2)²(2 – 13)³,where A; are the eigenvalues of A. Also, it is given thatdim N(A – 221) = dim N(A – A31I) = 2,where N(.) denotes the nullity of the operand. Find all possible Jordan canonical forms for A. Explainyour answer.

We can see Jordan canonical form of a matrix by the following theorem. Jordan decomposition theorem:…

Answered: Q2. Consider the homogeneous CLTI…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

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Consider the homogeneous CLTI system ?̇ = ??. The characteristic equation of ? is given by:
det(? − ??) = (? − ?3)(? − ?4)4(? − ?5)5,
where ?7 are the eigenvalues of ?. Also, it is given that
dim?(? − ?4?) = dim?(? − ?5?) = 2,
where ?(. ) denotes the nullity of the operand. Find all possible Jordan canonical forms for ?. Explain
your answer.

Q2. Consider the homogeneous CLTI system x
= Ax. The characteristic equation of A is given by:
det(A – A1) = (1 – 14)(1 – 2)²(2 – 13)³,
where A; are the eigenvalues of A. Also, it is given that
dim N(A – 221) = dim N(A – A31I) = 2,
where N(.) denotes the nullity of the operand. Find all possible Jordan canonical forms for A. Explain
your answer.

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