Let A and B be nn matrices, and assume that v in Rn is an eigenvector of A corresponding
Chapter 7, Problem 42(choose chapter or problem)
Let A and B be nn matrices, and assume that v in Rn is an eigenvector of A corresponding to the eigenvalue and also an eigenvector of B corresponding to the eigenvalue . (a) Prove that v is an eigenvector of the matrix AB. What is the corresponding eigenvalue? (b) Prove that v is an eigenvector of the matrix A+B. What is the corresponding eigenvalue?
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