(g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Need help with part (g). Thank you :)

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7. Let A =
(a) Find the characteristic polynomial of A.
(b) Find the eigenvalues of A.
(c) Find a basis for each eigenspace of A.
resour
(d) For each eigenvalue, state its algebraic and geometric multiplicity. Explain your answer.
(e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A.
(f) Is the conic section defined by the equation x" Ax = 1 an ellipse or an hyperbola? Why?
(g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A?
ourseHo
Transcribed Image Text:- } 7. Let A = (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A. resour (d) For each eigenvalue, state its algebraic and geometric multiplicity. Explain your answer. (e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A. (f) Is the conic section defined by the equation x" Ax = 1 an ellipse or an hyperbola? Why? (g) How many paths of length n exist between vertices 1 and 2 in the graph with adjacency matrix A? ourseHo
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