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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?

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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-13 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 22 of this polynomial. λ1 and 22 are called the eigenvalues of the matrix A. that Avi hivi. (c) For each eigenvalue λ1, find an eigenvector vi = = λ1 0 (d) Construct the matrix D = (2) 0 22 (x) + (8) such yi and the matrix Q whose columns are eigenvectors v1 and v2. Calculate QDQ¹; what do you notice? -1
Transcribed Image Text:-13 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 22 of this polynomial. λ1 and 22 are called the eigenvalues of the matrix A. that Avi hivi. (c) For each eigenvalue λ1, find an eigenvector vi = = λ1 0 (d) Construct the matrix D = (2) 0 22 (x) + (8) such yi and the matrix Q whose columns are eigenvectors v1 and v2. Calculate QDQ¹; what do you notice? -1
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