You are the given the eigenvectors u1 0 -2 of the matrix A given by -8-8-8-—-—- = 1 = U2 and = A 238373 23 130 13 13 13 10/30 (a) Find the eigenvalues λ₁, λ2 and A3 of the eigenvectors u̸₁, u̟2 and u̟3, respectively. λι λε X3 = == (b) The vectors u₁, u₂ and u3 form a basis B of R³. Let v be the vector -5 A Find the coordinate vector [V] B of v in the basis B. -0 [V]B (c) Calculate A20 v. Below, you can use exponentials to enter your answer, you don't have to write the full decimal expansion of the entries of the vector below, which could be large numbers. For instance, to write 5.920. 8, enter 5*9^(20)*8.
You are the given the eigenvectors u1 0 -2 of the matrix A given by -8-8-8-—-—- = 1 = U2 and = A 238373 23 130 13 13 13 10/30 (a) Find the eigenvalues λ₁, λ2 and A3 of the eigenvectors u̸₁, u̟2 and u̟3, respectively. λι λε X3 = == (b) The vectors u₁, u₂ and u3 form a basis B of R³. Let v be the vector -5 A Find the coordinate vector [V] B of v in the basis B. -0 [V]B (c) Calculate A20 v. Below, you can use exponentials to enter your answer, you don't have to write the full decimal expansion of the entries of the vector below, which could be large numbers. For instance, to write 5.920. 8, enter 5*9^(20)*8.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 31EQ
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![You are the given the eigenvectors u1
0
-2 of the matrix A given by
-8-8-8-—-—-
=
1
=
U2
and
=
A
238373
23
130 13
13 13 10/30
(a) Find the eigenvalues λ₁, λ2 and A3 of the eigenvectors u̸₁, u̟2 and u̟3, respectively.
λι
λε
X3
=
==
(b) The vectors u₁, u₂ and u3 form a basis B of R³. Let v be the vector
-5
A
Find the coordinate vector [V] B of v in the basis B.
-0
[V]B
(c) Calculate A20 v.
Below, you can use exponentials to enter your answer, you don't have to write the full decimal expansion of the entries of the vector below, which could be large numbers.
For instance, to write 5.920. 8, enter 5*9^(20)*8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1afc3bd-f5bd-4f69-961d-18bf898b97ca%2F4e7f7355-44bd-4c8c-8944-5bb283f5c8f3%2Fntfbece_processed.png&w=3840&q=75)
Transcribed Image Text:You are the given the eigenvectors u1
0
-2 of the matrix A given by
-8-8-8-—-—-
=
1
=
U2
and
=
A
238373
23
130 13
13 13 10/30
(a) Find the eigenvalues λ₁, λ2 and A3 of the eigenvectors u̸₁, u̟2 and u̟3, respectively.
λι
λε
X3
=
==
(b) The vectors u₁, u₂ and u3 form a basis B of R³. Let v be the vector
-5
A
Find the coordinate vector [V] B of v in the basis B.
-0
[V]B
(c) Calculate A20 v.
Below, you can use exponentials to enter your answer, you don't have to write the full decimal expansion of the entries of the vector below, which could be large numbers.
For instance, to write 5.920. 8, enter 5*9^(20)*8.
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