← Matrix A is factored in the form PDP each eigenspace. A = 21 2 122 1 1 3 2 = 2 2 0-2 2-1 0 2 Use the Diagonalization Theorem to find the eigenvalues of A and a basis for 500 0 1 0 0 0 1 1 8 1 1 1 1 1 4 1 2 3 1 8 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is B. In ascending order, the two distinct eigenvalues are ₁ = and A₂ =Bases for the corresponding eigenspaces are and respectively. A₂ = and A3 = Bases for the and {}, respectively. OC. In ascending order, the three distinct eigenvalues are λ₁ = corresponding eigenspaces are k
← Matrix A is factored in the form PDP each eigenspace. A = 21 2 122 1 1 3 2 = 2 2 0-2 2-1 0 2 Use the Diagonalization Theorem to find the eigenvalues of A and a basis for 500 0 1 0 0 0 1 1 8 1 1 1 1 1 4 1 2 3 1 8 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A. There is one distinct eigenvalue, λ = A basis for the corresponding eigenspace is B. In ascending order, the two distinct eigenvalues are ₁ = and A₂ =Bases for the corresponding eigenspaces are and respectively. A₂ = and A3 = Bases for the and {}, respectively. OC. In ascending order, the three distinct eigenvalues are λ₁ = corresponding eigenspaces are k
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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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.
A =
21 2
122
1 1 3
2
= 2
2
0-2
2-1 0
2
500
0 1 0
0 0 1
1
8
1
4
1
8
1
2
4
1
3
8 8 4
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A. There is one distinct eigenvalue, λ =
A basis for the corresponding eigenspace is {}
B. In ascending order, the two distinct eigenvalues are A₁ = and A₂ =Bases for the corresponding
eigenspaces are
and
respectively.
OC. In ascending order, the three distinct eigenvalues are λ₁
corresponding eigenspaces are O
^₂ = ₁ and 3²
and {}, respectively.
Bases for the
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