Question: (4) We are told that A and B are both it x n matrices and that '5' is an eigenvector for both A and B.

(4) We are told that A and B are both it x n matrices and that '5' is an eigenvector for both A and B. Let /\\1 be the eigenvalue associated with A and 17. Let A2 be the eigenvalue associated with B and '5'. (a) Show that 17 is an eigenvalue for the matrix AB. What is the eigenvalue associated with AB and 13'? (b) Part (a) can fail if 17 is an eigenvector of A but not an eigenvector of B. Give an example to show this, and justify your

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