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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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 20E
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Solve part A please
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.)
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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