Problem 1. Consider the matrix A= (1 6) (0.1) . (15 points) Calculate the eigenvalues and eigenvectors of the matrix A. . (10 points) Write down a closed expression of A " (1 ) and A. ( 8 ). Problem 2. You should explain how you get the answers you write down. . (10 points) Write down the rotation matrix R which describes the rotation around the line r = 1, y = -5 with the opposite orientation of the z-axis by 24/3 radians. . (10 points) Find the image of the points (3,5, -4), (3,4, -5) under the perspective projection with center of perspective at (r, y, z) = (0, 0, 10). . (5 points) Find the image of the point (1, 2,3) after first performing the above perspective projection and then the above rotation.Problem 3. . (15 points) Consider the following transition matrix 0.6 0.3 0 0 0 0.3 0.7 0.1 0 0 To = 0 0 0.9 0.1 0 0 0 0 0.6 0.3 0. 0 0 0.3 0.7 Draw the Markov chain described by 72. Is 72 a regular transition matrix? . (10 points) Does the system possess a unique steady state vector? If yes write it down explaining how you obtained it. If not explain why.e (15 points) Consider the following transition matrix 07 03 0 0 0 03 07 01 0 0 y=10 0 09 01 0 o 0 0 06 03 0 0 0 03 0.7 Draw the Markov chain described by 7). 1s T a regular transition matrix? e (10 points) Does the system possess a unique steady state vector? If yes write it down explaining how vou obtained it. If not explain why