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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. 1 8 4 8 2 2 1 2 2 5 0 0 3 A = 1 3 1 = 2 0 - 1 0 1 0 8 4 1 2 2 2 -2 0 0 1 1 1 4 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 2 = Bases for the corresponding eigenspaces are and {}. O C. In ascending order, the three distinct eigenyalues are M = and λ Bases for the corresponding eigenspaces are

Matrix A is factored in the form PDP . Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 1 8 4 8 2 2 1 2 2 5 0 0 3 A = 1 3 1 = 2 0 - 1 0 1 0 8 4 1 2 2 2 -2 0 0 1 1 1 4 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 2 = Bases for the corresponding eigenspaces are and {}. O C. In ascending order, the three distinct eigenyalues are M = and λ Bases for the corresponding eigenspaces are

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. 1 1 1 8 5 0 0 4 8 2 2 1 2 2 1 1 3 A = 1 3 1 2 - 1 0 1 0 8 4 8 1 2 2 2 0 0 1 1 1 1 4 2 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, = |. A basis for the corresponding eigenspace is { }. B. In ascending order, the two distinct eigenvalues are ^1 and 2 = . Bases for the corresponding eigenspaces are { and { }, respectively. %3D O C. In ascending order, the three distinct eigenvalues are 4 =, ^2 =, and 13 Bases for the corresponding eigenspaces are {);{), and {}. respectivelv.
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. 1 1 1 8 5 0 0 4 8 2 2 1 2 2 1 1 3 A = 1 3 1 2 - 1 0 1 0 8 4 8 1 2 2 2 0 0 1 1 1 1 4 2 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, = |. A basis for the corresponding eigenspace is { }. B. In ascending order, the two distinct eigenvalues are ^1 and 2 = . Bases for the corresponding eigenspaces are { and { }, respectively. %3D O C. In ascending order, the three distinct eigenvalues are 4 =, ^2 =, and 13 Bases for the corresponding eigenspaces are {);{), and {}. respectivelv.
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