Mathematics 38
Differential Equations
Examination 1
October 5, 2009
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1.
(5 points, answer only, no partial credit) Can the system below be solved by Cramer’s rule?
x
1
+
x
2
+
x
3
= 0
2
x
1
+3
x
2
+
x
3
= 0

x
1

3
x
2
+
x
3
= 0
2.
(5 points, answer only, no partial credit) Consider the following system of equations:
x
1
+
x
2
+
x
3
= 0
2
x
1
+3
x
2
+
x
3
= 0

x
1

3
x
2
+
x
3
= 0
Choose one answer: The system has
a.
a unique solution,
b.
no solution,
c.
more than 1 solution.
d.
None of the above.
3.
(5 points, answer only, no partial credit) Choose one answer.
det
5
1
sin
t
t
2
+ 3
1
0
4
e
t
e
t
0
0
0
3
ln
t
8
0
0
0
2
√
t
0
0
0
0
1
=
a.
5
,
b.
2
√
t
,
c.
120
,
d.
120

sin
t

1
4
e
t

1
4
(
t
2
+ 3)
e
t
.
e.
None of the above.
4.
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 Fall '10
 Hasselblatt
 Differential Equations, Equations, Derivative, Partial differential equation

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