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Let A be a matrix with the following factorisation into PDP-1: [-3 -5] [3 -5 -6 9 6 1 -1 -4 0 -3 0 -1 -6 -3 1 -1] Lo 3] L-1 10 Use this to find the eigenvalues of A and a basis for each eigenspace. Into e_1 enter the larger eigenvalue, and into A_1 enter a matrix whose columns form a basis of the corresponding eigenspace. Into e_2 enter the smaller eigenvalue, and into A_2 enter a matrix whose columns form a basis of the corresponding eigenspace.

Let A be a matrix with the following factorisation into PDP-1: [-3 -5] [3 -5 -6 9 6 1 -1 -4 0 -3 0 -1 -6 -3 1 -1] Lo 3] L-1 10 Use this to find the eigenvalues of A and a basis for each eigenspace. Into e_1 enter the larger eigenvalue, and into A_1 enter a matrix whose columns form a basis of the corresponding eigenspace. Into e_2 enter the smaller eigenvalue, and into A_2 enter a matrix whose columns form a basis of the corresponding eigenspace.

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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PDP^-1 Matrix 

Let A be a matrix with the following factorisation into PDP-l: -3 6. 6. -1 -5 6 1 -6 9. 6. -1 -4 -3 -1 1 1 6. -6 -3 3. 1 Use this to find the eigenvalues of A and a basis for each eigenspace. Into e_1 enter the larger eigenvalue, and into A_1 enter a matrix whose columns form a basis of the corresponding eigenspace. Into e_2 enter the smaller eigenvalue, and into A_2 enter a matrix whose columns form a basis of the corresponding eigenspace.
Transcribed Image Text:Let A be a matrix with the following factorisation into PDP-l: -3 6. 6. -1 -5 6 1 -6 9. 6. -1 -4 -3 -1 1 1 6. -6 -3 3. 1 Use this to find the eigenvalues of A and a basis for each eigenspace. Into e_1 enter the larger eigenvalue, and into A_1 enter a matrix whose columns form a basis of the corresponding eigenspace. Into e_2 enter the smaller eigenvalue, and into A_2 enter a matrix whose columns form a basis of the corresponding eigenspace.
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