Econometrics Review Questions

(7) Using partitioning compute the inverse of the following matrices;
1 0 0 0 1
2 3 0 0
2 0 0 0
0 1 0 0 1
5 2 0 0
B 0 0 1 0 1
C
0 0 0 1
D
0 0 4 3
0 0 1 0
0 0 0 1 0
1 1 1 0 1
0 0 3 2
0 1 0 0
(8) Find the rank of the following matrices
1 1 1
1 1 2 1
A
2 1 1
B 2 1 0 1
4 1 3
1 0 2 1
D 1 2
8 16
(9) Prove that
1 2 0
0 , 1 and
1
1 0 1
are linearly independent
(10) Let A and B be square invertible matrices of the same order. Solve for X in the
following equations;
t
(a) X A B
(b) 1 1
X A A B
(c) Solve for X in the preceding equation when
1 2 1
0 1 2
A 0 1 0
and B 1 0 1
3 1 2
1 1 1
(11)
mx
y
1
Given the system , compute m so that the system has;
x my 2m
1
(a) No solution
(b) Infinitely many solutions
(c) A unique solution
(d) A solution with x 3
(12)
kx y z 1
Consider the system x ky z 1 , use determinants to find those values of k for which
x y kz 1
the system has;
(a) A unique solution
(b) More than one solution
2