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122
APPENDIX D
SOLUTIONS TO PROBLEMS
D.1
(i)
016
21
7
2
0
61
2
180
4
5
0
5
36
24
300
⎛⎞
−−
⎛
⎞
⎜⎟
==
⎜
⎟
⎝⎠
⎝
⎠
AB
(ii)
BA
does not exist because
B
is 3
×
3 and
A
is 2
×
3.
D.3
Using the basic rules for transpose,
(
)()
()
′
′′
′
′
′
=
=
XX
X X
, which is what we wanted to
show.
D.5
(i) The
n
×
n
matrix
C
is the inverse of
AB
if and only if
C
(
AB
) =
I
n
and (
AB
)
C
=
I
n
.
We
verify both of these equalities for
C
=
B
1
A
1
.
First, (
B
1
A
1
)(
AB
) =
B
1
(
A
1
A
)
B = B
1
I
n
B
=
B
1
B
=
I
n
.
Similarly, (
AB
)(
B
1
A
1
) =
A
(
BB
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This note was uploaded on 09/11/2011 for the course ECONOMICS eco375 taught by Professor Suzuki during the Spring '11 term at University of Toronto.
 Spring '11
 Suzuki
 Econometrics

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