1 1 1 2. Consider the matrix J = 1 1 0 1 0 0 1 0| 1 (a) Interpreting J as an adjacency matrix for a graph with 4 nodes, labelled a, b, c, d in this order, draw the corresponding graph. (b) Specify all the walks which begin at node a and finish at node c using exactly 4 edges. As an example, one of the walks is a → b → c → d → c. Use this to deduce the value of the entry in row 1 and column 3 of Jª, clearly stating the theory that is being used. (c) From your answer to (b), specify the entry in row 1, column 4 of J³, giving a reason.
1 1 1 2. Consider the matrix J = 1 1 0 1 0 0 1 0| 1 (a) Interpreting J as an adjacency matrix for a graph with 4 nodes, labelled a, b, c, d in this order, draw the corresponding graph. (b) Specify all the walks which begin at node a and finish at node c using exactly 4 edges. As an example, one of the walks is a → b → c → d → c. Use this to deduce the value of the entry in row 1 and column 3 of Jª, clearly stating the theory that is being used. (c) From your answer to (b), specify the entry in row 1, column 4 of J³, giving a reason.
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
Problem 36EQ
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