following: a) Rewrite characteristic equation as polynomial of 3rd degree. b) Find the eigenvalues of matrix A c) Determine rank of Matrix A. Is matrix A invertible?
following: a) Rewrite characteristic equation as polynomial of 3rd degree. b) Find the eigenvalues of matrix A c) Determine rank of Matrix A. Is matrix A invertible?
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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Matrix method
![4. Suppose that A is a certain unspecified 3x3 matrix. Supposed that you are told that the
characteristic polynomial for A can be factored as p(2) = 2(2–1)(2– 2). Determine the
following:
a) Rewrite characteristic equation as polynomial of 3rd degree.
b) Find the eigenvalues of matrix A
c) Determine rank of Matrix A. Is matrix A invertible?
d) Determine rank of matrix (A-I), where I is an identity matrix of the same size as A.
e) Determine rank of matrix (A-2*I)
If in c)-e) it is impossible to determine the rank of some of the above matrices,
explain why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b54814-b8b7-4677-bd95-e192d8c9023d%2Fec70de64-a287-4418-8f8f-fce2ce2d4fa8%2Fyqrkyui_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Suppose that A is a certain unspecified 3x3 matrix. Supposed that you are told that the
characteristic polynomial for A can be factored as p(2) = 2(2–1)(2– 2). Determine the
following:
a) Rewrite characteristic equation as polynomial of 3rd degree.
b) Find the eigenvalues of matrix A
c) Determine rank of Matrix A. Is matrix A invertible?
d) Determine rank of matrix (A-I), where I is an identity matrix of the same size as A.
e) Determine rank of matrix (A-2*I)
If in c)-e) it is impossible to determine the rank of some of the above matrices,
explain why.
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