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...
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...
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)...
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...
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...