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Mathematical Economics Midterm #1, October 2, 2000
You have until 4:45 to complete this exam. Answer all fve questions. Each question is worth
20 points, For a total oF 100 points. Good luck!
1. (Linear Systems) Consider the linear system
x
+
y
+
z
= 13
x
+ 5
y
+ 10
z
= 61
.
Show that this system has solutions.
How many solutions are there?
Can you fnd a
solution where
x
,
y
, and
z
are all positive integers?
2. (Matrices) Let
A
and
B
be
n
×
n
matrices. Show that iF (
A
+
B
)
2
=
A
2
+ 2
AB
+
B
2
,
then
AB
=
BA
.
3. (Determinant) Consider the matrix
A
=
±
3

4

1
0
²
±ind all
λ
so that det(
A

λI
) = 0.
4. (Linear Systems) Demand For good 1 is
e
1

ap
1
+
bp
2
; demand For good 2 is
e
2
+
cp
1

dp
2
;
the supply oF good
i
is
s
i
. Here
a
,
b
,
c
,
d
,
e
i
, and
s
i
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This note was uploaded on 01/01/2012 for the course ECO 7405 taught by Professor Staff during the Fall '08 term at FIU.
 Fall '08
 STAFF
 Economics

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