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  1. R

    Stuck on expressing a complex number in the form (a+bi)

    Yes I meant, exponent, didn't catch that till later.
  2. R

    Trying to find long run behaviour of a dynamical system

    Sorry, I didn't know what the normal convention was. I simply posted what I was taught. Thanks, will do so in the future.
  3. R

    Trying to find long run behaviour of a dynamical system

    Yes, I looked at that exact article, but it seems way beyond what we've learned. I'm not even able to decipher it unfortunately. As for your suggestion, well, the entire problem is that I do not know x(0). Will a 2x2 (P*P) give me the same answer as P2?
  4. R

    Trying to find long run behaviour of a dynamical system

    Searched on google, and we haven't learned it, so I'm guessing we can solve this without equilibrium distribution.
  5. R

    Finding transition matrix, no % probability given

    It's the correct answer! Thank you!
  6. R

    Trying to find long run behaviour of a dynamical system

    Thanks for the reply. What do you mean by "standard equilibrium (or limiting) equations"? I haven't come across these terms.
  7. R

    Finding transition matrix, no % probability given

    P would be the transition matrix, with 1,2,3 as states
  8. R

    Finding transition matrix, no % probability given

    Imagine a 1 above the 1st column, a 2 above the 2nd column, and 3 above the 3rd column do the same for the rows (1 beside the 1st row...) and Pij = changing from state j to state i Basically I put 0.875 in the 2nd row and 1st column, because the transition from state 1 to 2 is 7x more likely...
  9. R

    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...
  10. R

    Trying to find long run behaviour of a dynamical system

    By the way, the transition matrix is: \begin{bmatrix}0.15 & 0.25 \\ 0.85 & 0.75 \end{bmatrix}
  11. R

    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...
  12. R

    Stuck finding a specific value of an inverse of a complex matrix

    I just realized my mistake, it was arithmetic.
  13. R

    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)...
  14. R

    Stuck on expressing a complex number in the form (a+bi)

    Thanks for the reply. So you're saying it's not the top left quadrant? Which quadrant is it it then?
  15. R

    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...
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    How do I find the eigenvalue given unknown rows & eigen vect

    I have 5 minutes left to answer the question. Would you mind helping me with the answer, and then you can explain it to me?
  17. R

    How do I find the eigenvalue given unknown rows & eigen vect

    An eigenvector of A is a non-zero vector x such that Ax = λx
  18. R

    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...
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