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1. ### Finding transition matrix, no % probability given

Homework Statement 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 7 times more likely to go to State 2 at the next step than to State...
2. ### Trying to find long run behaviour of a dynamical system

Homework Statement 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 85% chance that they will not get the flu in the following year. If they don't have a flu in a given year then...
3. ### Stuck finding a specific value of an inverse of a complex matrix

Homework Statement Consider the following matrix. A = 2 + 4i.........1 + 5i 2 − 3i.........2 + 3i Let B = A-1. Find b12 (i.e., find the entry in row 1, column 2 of A−1) Homework Equations A-1 = 1/(ad - cb)* [ d -b ] [ -c a ] <--imagine as 2x2 matrix with first row (d,-b)...
4. ### Stuck on expressing a complex number in the form (a+bi)

Homework Statement Express the complex number (−3 +4i)3 in the form a + bi Homework Equations z = r(cos(θ) + isin(θ)) The Attempt at a Solution z = -3 + 4i z3 = r3(cos(3θ) + isin(3θ)) r = sqrt ((-3)2 + 42) = 5 θ = arcsin(4/5) = 0.9273 ∴ z3 = 53(cos(3⋅0.9273) + isin(3⋅0.9273)) a = -117 b...
5. ### How do I find the eigenvalue given unknown rows & eigen vect

Homework Statement Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. A = 4 4 2 * * * * * * x = 2 -1 10 Given that x is an eigenvector of the matrix A, what is the corresponding eigenvalue? Homework Equations The Attempt at a Solution 4−λ 4 2 a...