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Matrix A is factored in the form PDP¯1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 20 - 12 -4 0 - 1 5 0 0 0 0 1 A = 6 5 24 1 2 0 5 0 2 1 8 = 0 0 1 0 0 2 -10 - 4 ..... Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, 1 = A basis for the corresponding eigenspace is { }. O B. In ascending order, the two distinct eigenvalues are = and 12 = Bases for the corresponding eigenspaces are { } and {}, respectively. O C. In ascending order, the three distinct eigenvalues are 1 = ,^2 = and 13 = Bases for the corresponding eigenspaces are { }, { }, and }, respectively.

Matrix A is factored in the form PDP¯1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 20 - 12 -4 0 - 1 5 0 0 0 0 1 A = 6 5 24 1 2 0 5 0 2 1 8 = 0 0 1 0 0 2 -10 - 4 ..... Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, 1 = A basis for the corresponding eigenspace is { }. O B. In ascending order, the two distinct eigenvalues are = and 12 = Bases for the corresponding eigenspaces are { } and {}, respectively. O C. In ascending order, the three distinct eigenvalues are 1 = ,^2 = and 13 = Bases for the corresponding eigenspaces are { }, { }, and }, respectively.

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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Matrix A is factored in the form PDP'. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 2 0 12 - 4 0 - 1 5 0 0 1 A = 6 5 24 1 0 5 0 1 0 0 1 0 0 2 - 1 0 - 4 ..... Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, 1 = A basis for the corresponding eigenspace is { }. ОВ. In ascending order, the two distinct eigenvalues are 11 = and A2 = . Bases for the corresponding eigenspaces are and { }, respectively. C. In ascending order, the three distinct eigenvalues are 1 = , 12 = and A3 = Bases for the corresponding eigenspaces are and }, respectively.
Transcribed Image Text:Matrix A is factored in the form PDP'. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 2 0 12 - 4 0 - 1 5 0 0 1 A = 6 5 24 1 0 5 0 1 0 0 1 0 0 2 - 1 0 - 4 ..... Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, 1 = A basis for the corresponding eigenspace is { }. ОВ. In ascending order, the two distinct eigenvalues are 11 = and A2 = . Bases for the corresponding eigenspaces are and { }, respectively. C. In ascending order, the three distinct eigenvalues are 1 = , 12 = and A3 = Bases for the corresponding eigenspaces are and }, respectively.
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