The characteristic polynomial of an n x n matrix is the polynomial p(x) = det(A - I). (a) Find the characteristic polynomial p(x) = x² + c₁x + co for the matrix A = (b) With A as in the previous part, evaluate p(A). That is, what is A2 + c₁A+ Col₂ =? (co and c₁ are the same coefficients you found in part (a) as well.)
The characteristic polynomial of an n x n matrix is the polynomial p(x) = det(A - I). (a) Find the characteristic polynomial p(x) = x² + c₁x + co for the matrix A = (b) With A as in the previous part, evaluate p(A). That is, what is A2 + c₁A+ Col₂ =? (co and c₁ are the same coefficients you found in part (a) as well.)
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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Solve part A please
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2. The characteristic polynomial of an n x n matrix is the polynomial p(x) = det(A = xI).
(a) Find the characteristic polynomial p(x) = x² + €₁x + co for the matrix A =
(b) With A as in the previous part, evaluate p(A). That is, what is A² + c₁A+ Col₂ =?
(co and c₁ are the same coefficients you found in part (a) as well.)"
Transcribed Image Text:MAT2114 HOMEWORK 07
2. The characteristic polynomial of an n x n matrix is the polynomial p(x) = det(A = xI).
(a) Find the characteristic polynomial p(x) = x² + €₁x + co for the matrix A =
(b) With A as in the previous part, evaluate p(A). That is, what is A² + c₁A+ Col₂ =?
(co and c₁ are the same coefficients you found in part (a) as well.)
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