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Consider a matrix A = a C where a, b, c are real numbers such that abc = 1 and a² + b² + c? = 3. (a) Determine the eigenvalues of A. (b) Now, consider the case when a 1. For this case, determine what should the values of b and c be so that the following vector is an eigenvector of A: 1 K = 3 (c) Now, consider the case when a = b = c = 1, so that 1 1 A = 1 1 1 For this case, determine an orthogonal matrix P that diagonalizes A, such that the first column of P is given by V2 C = V2 Downl

Consider a matrix A = a C where a, b, c are real numbers such that abc = 1 and a² + b² + c? = 3. (a) Determine the eigenvalues of A. (b) Now, consider the case when a 1. For this case, determine what should the values of b and c be so that the following vector is an eigenvector of A: 1 K = 3 (c) Now, consider the case when a = b = c = 1, so that 1 1 A = 1 1 1 For this case, determine an orthogonal matrix P that diagonalizes A, such that the first column of P is given by V2 C = V2 Downl

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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Consider the matrix in the image and please answer b and c.

 

Consider a matrix A = a C where a, b, c are real numbers such that abc = 1 and a2 + 62 + c2 = 3. (a) Determine the eigenvalues of A. (b) Now, consider the case when a 1. For this case, determine what should the values of b and c be so that the following vector is an eigenvector of A: ()-- -() 1 K = 2 3 (c) Now, consider the case when a = b = c = 1, so that 1 1 A = 1 1 1 1 For this case, determine an orthogonal matrix P that diagonalizes A, such that the first column of P is given by V2 C = V2 Downl
Transcribed Image Text:Consider a matrix A = a C where a, b, c are real numbers such that abc = 1 and a2 + 62 + c2 = 3. (a) Determine the eigenvalues of A. (b) Now, consider the case when a 1. For this case, determine what should the values of b and c be so that the following vector is an eigenvector of A: ()-- -() 1 K = 2 3 (c) Now, consider the case when a = b = c = 1, so that 1 1 A = 1 1 1 1 For this case, determine an orthogonal matrix P that diagonalizes A, such that the first column of P is given by V2 C = V2 Downl
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