Problem #1: Consider a quantum mechanical system with three states. At each step a particular particle transitions from one state to a different state. Empirical data show that if the particle is in State 1, then it is 2 times more likely to go to State 2 at the next step than to State 3. If it is in State 2, then it is 9 times more likely to go to State 3 at the next step than to State 1. If it is in State 3 then it is equally likely to go to State 1 or State 2 at the next step. Let A be transition matrix for this markov chain. Find a3, a3y, and as3 (ie., find the last row in the transition matrix) Problem #3: (a) Express the complex number (-2 +5i) in the form a + bi. (b) Express the below complex number in the form a + bi. 2+ 40 i(2+50) (c) Consider the following matrix. A 1+2i 0-3i T13-2i 242 Let B=A"!. Find byy (i.e., find the entry in row 1, column 1 of A_l) Problem #3(a): I:I if your answer is a + bi, then enter a,b in the answer box Enter your answer symbolically, ) . i . Problem #3(b): as in these examples if your answer is @ + bi, then enter a,b in the answer box Problem #3(c): as in these examples if your answer is @ + bi, then enter a,b in the answer box ' Just Save | | Submit Problem #3 for Grading | Problem #3 | Attempt #1 Attempt #2 Attempt #3 Your Answer: | 3(a) 3(a) 3(a) 3(b) 3(b) 3(b) 3(c) 3(c) 3(c) Your Mark: | 3(a) 3(a) 3(a) 3(b) 3(b) 3(b) 3(c) 3(c) 3(c) Problem #4: Which of the following is a solution to the equation D= (\\/5 -10)? (A) 213 [cos(10719) + i sin(1079)] (B) 2'[cos(1179) + i sin(117/9)] (C) 213 [cos(87/9) + i sin(87/9)] (D) 213 [cos(1377/18) + i sin(137/18)] (E) 213[cos(17m/18) + i sin(177/18)] (F) 2'3[cos(2377/18) + i sin(237/18)] (G) 213[cos(7Tm/9) + i sin(77/9)] (H) 2!3[cos(197/18) + i sin(197/18)] Problem #4: ' Just Save | | Submit Problem #4 for Grading