Suppose that is an eigenvector for both the matrix A and the matrix B, with corresponding eigenvalue X for A and corresponding eigenvalue μ for B. Show that is an eigenvector of A + B and AB. Proof: Since Au Au and Bu= μv: (i) (A + B) = and (ii) ABv A. Au + Bu B. A(Bv) = A(μv) C. λΰ + μύ D. (λ +μ) E. λμυ F. μ(Av) = μ(xv) Q.E.D.

Q: and find the corresponding eigenvector.

A: λ is an eigen value if we have Av=λv for some v non-zero.v is called eigen vector.

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