Econometrics Review Questions

(i) Int B B B
(ii) B 2 B B
(iii) B
is bounded
(iv)
(v)
B is closed if and only if B is open
B is bounded if and only if B is not bounded
B Bis open
(vi) B is closed if and only if
(vii) B is closed if and only if B
B
(18)
3x 3y z 0
Given the homogenous system 4x 2y mz 0 ,
3x 4y 6z
0
(a) Compute m so that it has no trivial solution and
(b) Solve it for that value
Q x, y, z x 2axy y z 2axz
(19) Given the quadratic form
2 2 2
(a) Determine for what values of a , the quadratic form Q is positive definite
(b) Determine for what values of a , the quadratic form Q is positive indefinite
(20) Solve the differential equation
dy 45
dt 2000 5t
y 80
(21) (i) Solve the differential equation of the logistic type given as P kPM P
where k
and M are positive constants.
(ii) How would the solution in (i) above change given the initial condition 0
P
0
P
3 ln 1, 0, satisfying 1 2
(22) Find the particular solution of xy y x x y
(23) Find the general solution of
xy 2y x
2
(24) Solve the equation
dy
3 , 0
dx
2
x x y x
(25) Find the solution to the differential equation dy xy x which satisfies 3 0
dx y when x
4