Let G be a bipartite graph with adjacency matrix A. (a) Show that A is not primitive

Chapter 4, Problem 4.6.37

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Let G be a bipartite graph with adjacency matrix A. (a) Show that A is not primitive. (b) Show that if l is an eigenvalue of A, so is l. [Hint: Use Exercise 78 in Section 3.7 and partition an eigenvector for l so that it is compatible with this partitioning of A. Use this partitioning to find an eigenvector for l.] 3

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