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EC 469/569: Introduction to Econometrics
Problem Set
1
Due: Monday, January
2
2
1.1. A scientist is studying the effect that oat bran has on his cholesterol level. In order to analyze
this issue, he collects information each month on his cholesterol level and the number of grams of
oat bran that he eats each month. Is this cross section data, time series data, panel data or none
of these?
1.2. Consider the following matrix and vector:
M1=
[
10 7
7 5
]
and V1=
[
4
5
]
(a.) What is the dimension of M1? What is the dimension of V1?
(b.) Would it be possible to compute the product M1×V1? Explain why or why not.
(c.) Would it be possible to compute the product V1×M1? Explain why or why not.
(d.) Write out M1’. Write out V1’. What is the dimension of V1’ ?
(e.) Compute the product V1’×M1. Show all work.
(f.) Compute M1−1 and V 1−1. Show all work.
(g.) Compute M1−1 × V 1. Show all work.
1.3. Present (a) the transpose, (b) the determinant, (c) the rank, (d) the inverse of each matrix (if
it exists), and (e) put it in a row echelon form. Is each matrix full rank? Show your work.
A =
[
5
]
; B =
[
1 4
7 3
]
; C =
1 2 23 2 1
0 3 2
;
D =
1 2 3
4 5 6
7 8 9
10 11 12
; E =
1 0 53 2 2
1 4 7
;
F =
[
1 2 3 4
]
;
G =
1 1
1 2
1 3
1 4
;
1.4. Perform the following matrix operations.Write the dimensions of each matrix and show your
work.
A =
1 1
1 2
1 3
1 4
+
1 1
1 2
1 3
1 4
; B =
[
1 4 3
2 5 6
]
+
1 09 1
5 2
; C =
10 4 22 5 6
1 3 1
+
1 0 29 1 4
5 2 5
;
D =
1 1
1 2
1 3
1 4
−
1 1
1 2
1 3
1 4
; E =
1 4 3 9
2 5 6 4
8 5 0 4
4 7 7 2
−
1 0 12 3
9 1 1 4
5 2 3 9
2 0 1 6
; F =
10 4 22 5 6
1 3 1
−
1 0 29 1 4
5 2 5
;
1
G =
1 0 0 10 1 0 2
0 0 1 1
·
1 1
1 2
1 3
1 4
; H = [1 1 1 1] ·
1 1
1 2
1 3
1 4
; J =
1 11 2
1 3
· [1 0 0
0 2 0
]
;
K =
1 0 00 2 0
0 0 3
·
1 11 2
1 3
1.5. Look at the following matrices and verify whether each of them is: symmetric, diagonal, idem-
potent, square, scalar, identity, triangular, singular, full-rank.
A =
1 0 00 1 0
0 0 1
; B = [1 2 3
2 4 6
]
; C =
1 2 31 0 1
3 4 7
2
