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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
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.
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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