24 -8 15 Consider the matrix A = (a) Calculate the det(A − xI), where x is a variable. We call the result the characteristic polynomial of A. (b) Give the two zeros 1 and 2 of this polynomial. λ1 and 22 are called the eigenvalues of the matrix A. that Avi hivi. -13 = (c) For each eigenvalue λ1, find an eigenvector vi = | 0 ( 0 λ2 are eigenvectors v1 and v2. Calculate QDQ (d) Construct the matrix D = = () ()such # yi λ1 and the matrix Q whose columns what do you notice?

24 -8 15 Consider the matrix A = (a) Calculate the det(A − xI), where x is a variable. We call the result the characteristic polynomial of A. (b) Give the two zeros 1 and 2 of this polynomial. λ1 and 22 are called the eigenvalues of the matrix A. that Avi hivi. -13 = (c) For each eigenvalue λ1, find an eigenvector vi = | 0 ( 0 λ2 are eigenvectors v1 and v2. Calculate QDQ (d) Construct the matrix D = = () ()such # yi λ1 and the matrix Q whose columns what do you notice?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 36E

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