1. (1 point) LetA = [8 2 ] andvi =[2 ]. 2-[3] i) Matrix A =_ _ ] vectors of A. ii) The eigenvalues of A: [Note: If there is more than one answer, separate them by commas. E.g. 1,2] Determine the corresponding eigenvalues. 5. (1 point) Suppose that v is an eigenvector for both the 21 = - for eigenvector vi matrix A and the matrix B, with corresponding eigenvalue a for A and corresponding eigenvalue u for B. 2= . for eigenvector v2 Show that i is an eigenvector of A + B and AB. 2. (1 point) Proof: For each of the following, determine whether v is an eigen- vector of the matrix A. Since AV = Av and BV = Wv: (i) ( A + B ) v = ? = 2 =2. 21. A = 30 0 = 3 and 2 2. A = -33 26 -39 32 , V= (ii) ABV = ? = 2 =2 2 3. A = -14 -8 16 10 ,V = Note: Due to the nature of the problem, only 1 attempt is Q.E.D. given. 3. (1 point) Find the three distinct real eigenvalues of the 8 6 6 matrix B = O 0 0 A. Luv The eigenvalues are B. AV+ BV [Note: If there is more than one answer, separate them by commas. E.g. 1,2] C. H(AV) = H(AV) 4. (1 point) Consider the diagonal matrix A = ) , where D. (2 + 1 ) V a