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 - 150 0 1-5 0 -15 00A= 6 5 300 10 502 1 100 051 0 00 0 2-1 0 -5.....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, ) =D. A basis for the corresponding eigenspace is }:B. In ascending order, the two distinct eigenvalues are i, = and , =Bases for the corresponding eigenspaces areand, respectively.C. In ascending order, the three distinct eigenvalues are A, =, 2 =], and Ag =Bases for the corresponding eigenspaces areandrespectively.

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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 - 15 A= 65 30 -0 1 2 00 5 50 0 o 0 1 0 5 0 2 1 10 -10 -5 -5 0 -1 10 0 0 0 2 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 coresponding eigenspace is In ascending order, the two distinct eigenvalues are 2, = and i, = | В. Bases for the corresponding eigenspaces are and {}. respectively. O C. In ascending order, the three distinct eigenvalues are , =, 2 =, and Ag =. 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 - 15 A= 65 30 -0 1 2 00 5 50 0 o 0 1 0 5 0 2 1 10 -10 -5 -5 0 -1 10 0 0 0 2 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 coresponding eigenspace is In ascending order, the two distinct eigenvalues are 2, = and i, = | В. Bases for the corresponding eigenspaces are and {}. respectively. O C. In ascending order, the three distinct eigenvalues are , =, 2 =, and Ag =. Bases for the corresponding eigenspaces are )., and ). respectively.

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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Question

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 - 15
0 0 1
-5 0 -1
5 00
A= 6 5 30
0 1
0 50
2 1 10
0 0
5
1 0 0
0 0 2
-1 0 -5
.....
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, ) =D. A basis for the corresponding eigenspace is }:
B. In ascending order, the two distinct eigenvalues are i, = and , =
Bases for the corresponding eigenspaces are
and
, respectively.
C. In ascending order, the three distinct eigenvalues are A, =, 2 =], and Ag =
Bases for the corresponding eigenspaces are
and
respectively.

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