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Problem 5. Consider the matrix 0.6 0.3 A = 0.4 0.7 1. Find the eigenvalues A1, 12 and eigenvectors v1, V2 of A. [0.5] 2. Let Xo = 0.5 . Verify that Xo may be written in the form Xo = CIV1 + 2V2 for some C1, C2. 3. Compute Xk = A*xo and show that Xk 3/7 (4/7 as * + 0o.0.5 0.2 0.3 0.3 Problem 6. Let A = 0.3 0.8 0.3 , V1= 0.6 , V2 = V3 0.2 0 0.4 0.1 2 1. Show that V1, V2, V3 are eigenvectors of A and find the corresponding eigenvalues. 0.17 2. Let Xo = 0.1 . Verify that xo may be written in the form Xo = CIV1 + C2V2 + C3V3 for some 0.8 C1, C2, C3. 3. Compute Xk = A*xo and find the limit as k - oo of Xk