[1 2 3] 9. Let A = |2 2 2. oute was SCourseHoto.com 3 2 1 (a) Explain why A is orthogonally diagonalizable. (b) The vectors V1 = (1,1, 1), v2 = (-1,0,1), and V3 = eigenvalues of A? %3D %3D ectors of A. What are the (c) Find a matrix Q which orthogonally (d) Let P = A. Explain why P is a regular stochastic matri: (e) What is the stationary distribution of P? (f) Consider the graph G with adjacency matrix A, and let m be an even natural number. What is the number of walks of length m between vertices 2 and 3?
[1 2 3] 9. Let A = |2 2 2. oute was SCourseHoto.com 3 2 1 (a) Explain why A is orthogonally diagonalizable. (b) The vectors V1 = (1,1, 1), v2 = (-1,0,1), and V3 = eigenvalues of A? %3D %3D ectors of A. What are the (c) Find a matrix Q which orthogonally (d) Let P = A. Explain why P is a regular stochastic matri: (e) What is the stationary distribution of P? (f) Consider the graph G with adjacency matrix A, and let m be an even natural number. What is the number of walks of length m between vertices 2 and 3?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Need help with parts (a), (b) and (c). Thank you :)
Transcribed Image Text:|1 2 3
9. Let A =
2 2 2
3 2 1
(a) Explain why A is orthogonally diagonalizable.
(b) The vectors vị =
(1,1, 1), v2 = (-1,0, 1), and v3 =
eigenvalues of A?
are
ctors of A. What are the
(c) Find a matrix Q which orthogonally diagonalizes A.
hutes was
(d) Let P
A. Explain why P is a regular stochastic matrix
(e) What is the stationary distribution of P?
(f) Consider the graph G with adjacency matrix A, and let m be an even natural number. What is the
number of walks of length m between vertices 2 and 3?
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