The matrix A = 3 - 3 6 are e v₁ = (1, 1) and v₂ = (1, 2). Use these values to diagonalize A as A = PDP-¹. P = D = P-1 = has eigenvalues X₁ = 0 and X₂ = 3. The associated eigenvectors - Now use the diagonalized form to calculate A80. The answer involves a factor of ( − 3)80 in each entry. Provide your answer in exact form with this scalar factored out. A80 = (-3)80 x
The matrix A = 3 - 3 6 are e v₁ = (1, 1) and v₂ = (1, 2). Use these values to diagonalize A as A = PDP-¹. P = D = P-1 = has eigenvalues X₁ = 0 and X₂ = 3. The associated eigenvectors - Now use the diagonalized form to calculate A80. The answer involves a factor of ( − 3)80 in each entry. Provide your answer in exact form with this scalar factored out. A80 = (-3)80 x
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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![The matrix A
are v₁ = (1, 1) and 2
P =
D =
[3 =3]
6
P
Use these values to diagonalize A as A
=
-
=
has eigenvalues A₁ = 0 and X₂:
-
=
80
A80 = ( − 3) X
: (1, 2).
PDP-¹.
3. The associated eigenvectors
Now use the diagonalized form to calculate 480. The answer involves a factor of ( − 3)80 in each
entry. Provide your answer in exact form with this scalar factored out.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fdef185-de8b-42f5-933e-8018dcf36541%2F778fb64f-55ba-405e-8913-c8854f2a3659%2Fyhbxkdr_processed.png&w=3840&q=75)
Transcribed Image Text:The matrix A
are v₁ = (1, 1) and 2
P =
D =
[3 =3]
6
P
Use these values to diagonalize A as A
=
-
=
has eigenvalues A₁ = 0 and X₂:
-
=
80
A80 = ( − 3) X
: (1, 2).
PDP-¹.
3. The associated eigenvectors
Now use the diagonalized form to calculate 480. The answer involves a factor of ( − 3)80 in each
entry. Provide your answer in exact form with this scalar factored out.
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