Plz help.

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 a33 (i.e., find the last row in the transition matrix) [ ot ecamptag et Problem #1: as in these examples separate your answers with a comma | Just Save ' ' Submit Problem #1 for Grading Problem #1 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #2: In any given year a person may or may not get the flu. Past records show that if a person has the flu one year then (due to a build up of antibodies) there is a 75% chance that they will not get the flu in the following year. If they don't have a flu in a given year then there is a 30% chance that they will get the flu the following year. (a) If a person has the flu one year, what is the probability that they will also have the flu 2 years later? (b) In the long run, what proportion of years does a person have the flu? enter your answer as an exact fraction, e.g., 22/37 enter your answer as an exact fraction, e.g., 22/37 | Just Save ' ' Submit Problem #2 for Grading | Problem #2 | Attempt #1 Attempt #2 Attempt #3 Your Answer: | 2(a) 2(a) 2(a) 2(b) 2(b) 2(b) Your Mark: | 2(a) 2(a) 2(a) 2(b) 2(b) 2(b) Problem #3: (a) Express the complex number (-2 +5i)3 in the form a + bi. (b) Express the below complex number in the form a + bi. 2+ 4 i(2+50) () Consider the following matrix. A 1+2i 0-3i T [3-2i 2420 LetB=A"'. Find by (i.e., find the entry in row 1, column 1 of A1 Problem #3(a): I:I if your answer is @ + bi, then enter a,b in the answer box Problem #3(b): as in these examples if your answer is a + bi, then enter a,b in the answer box poblem w30 [ ] e e it is 2+ bi, th binth b roblem #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(0) 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 2= (-\\/5 -0? (A) 213[cos(107/9) + i sin(107/9)] (B) 2!3[cos(1179) + i sin(117/9)] (C) 213[cos(87w/9) + i sin(87/9)] (D) 213[cos(13/18) + i sin(1377/18)] (E) 213[cos(17/18) + i sin(177/18)] (F) 21/3[cos(237/18) + i sin(2377/18)] (G) 213[cos(7m/9) + i sin(77/9)] (H) 213[cos(197/18) + i sin(197/18)] Problem #4: ' Just Save ' | Submit Problem #4 for Grading Problem #4 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #5: Express ( - % + ? i) 4 in the form a + bi. Enter the values of @ and b (in that order) into the answer box below, separated with a comma. povem s [ | e el is 2+ bi, th binth b roblem : as in these examples if your answer is & + bi, then enter a,b in the answer box | Just Save ' | Submit Problem #5 for Grading Problem #5 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: A linear dynamical system can be created for two masses connected by springs between one another, and connected to opposing walls. The state vector at time is a 4 x 1 vector consisting of the displacement and velocity of each of the two masses. The transition matrix for this dynamical system is given by the following matrix. 9 1 0 100 0 9 0 1 0 100 _9 9 T 10 1 0 9 _9 Because the system oscillates, there will be complex valued eigenvalues. Find the eigenvalue associated with the following eigenvector. i i V30 ~V/30 Problem #6: as in these examples if your answer is & + bi, then enter a,b in the answer box | Just Save ' | Submit Problem #6 for Grading Problem #6 | Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #7: Find the values of c1, C2, and c3 so that c1 (1, -4, -2) + c2 (2, -4,0) + c3 (1,0,0) = (-1,-16, 8). Problem #7: enter the values of C1, C2, and C3, separated by commas Just Save Submit Problem #7 for Grading Problem #7 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark