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(b) If p(t) = co + c₁t+c₂t² + ... + Cnt", define p(4) to be the matrix formed by replacing each power of t in p(t) by the corresponding power of A (with Aº = 1). That is, p(A) = col+c₁A+₂4² ++CnAn Show that if X is an eigenvalue of A, then one eigenvalue of p(A) is p(x).

(b) If p(t) = co + c₁t+c₂t² + ... + Cnt", define p(4) to be the matrix formed by replacing each power of t in p(t) by the corresponding power of A (with Aº = 1). That is, p(A) = col+c₁A+₂4² ++CnAn Show that if X is an eigenvalue of A, then one eigenvalue of p(A) is p(x).

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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(b) If p(t) = co + c₁t+c₂t² + ... + Cnt", define p(4) to be the matrix formed by replacing each power of t in p(t) by the corresponding power of A (with Aº = 1). That is, p(A) = col+c₁A+₂4² ++CnAn Show that if X is an eigenvalue of A, then one eigenvalue of p(A) is p(x).
Transcribed Image Text:(b) If p(t) = co + c₁t+c₂t² + ... + Cnt", define p(4) to be the matrix formed by replacing each power of t in p(t) by the corresponding power of A (with Aº = 1). That is, p(A) = col+c₁A+₂4² ++CnAn Show that if X is an eigenvalue of A, then one eigenvalue of p(A) is p(x).
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