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.

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A: according to guidelines we can solved only first 3 subparts thank you   We have the eigen values of…

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A: Step 1:Step 2:Step 3:Step 4: