Answer: Consider an n × n matrix A with the property that
Chapter 5, Problem 30E(choose chapter or problem)
Problem 30E
Consider an n × n matrix A with the property that the column sums all equal the same number s. Show that s is an eigenvalue of A. [Hint: Use Exercises 27 and 29.]
Reference Exercises 27:
Show that is an eigenvalue of A if and only if
is an eigenvalue of AT . [Hint: Find out how
T
are related.]
Reference Exercises 29:
Consider an n × n matrix A with the property that the row sums all equal the same number s. Show that s is an eigenvalue of A. [Hint: Find an eigenvector.]
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