9. 2 0 1. Consider the matrix A 18 -3 0 viewed as an operator on C³. 5 2 4 (a) Find the characteristic polynomial and the eigenvalues of A. (b) Find a basis of each eigenspace E(^, A) of A. (c) Find a basis B of C3 so that the matrix representation of A with respect to B is in the Jordan canonical form 3 Ј — (The basis B above is called a Jordan basis.)
9. 2 0 1. Consider the matrix A 18 -3 0 viewed as an operator on C³. 5 2 4 (a) Find the characteristic polynomial and the eigenvalues of A. (b) Find a basis of each eigenspace E(^, A) of A. (c) Find a basis B of C3 so that the matrix representation of A with respect to B is in the Jordan canonical form 3 Ј — (The basis B above is called a Jordan basis.)
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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PLEASE ANSWER PART B.
Transcribed Image Text:9.
2 0
1. Consider the matrix A
18 -3 0
viewed as an operator on C³.
5
2
4
(a) Find the characteristic polynomial and the eigenvalues of A.
(b) Find a basis of each eigenspace E(^, A) of A.
(c) Find a basis B of C3 so that the matrix representation of A with
respect to B is in the Jordan canonical form
3
Ј —
(The basis B above is called a Jordan basis.)
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