1
THE UNIVERSITY OF WESTERN ONTARIO
Department of Applied Mathematics
London
Ontario
Applied Mathematics 025b
First Tutorial Test – January 31, 2008
60 min
Name:
Solution
Section 2
(1)
Closed book. Only simple calculators are allowed. Print your name above
and student number on the page 2. Justify answers by showing sufficient
work to get the full marks. Solve each problem in space provided for that
specific problem.
Use margins or back of each sheet to do your rough
work.
Instructor – Dr. N. Kiriushcheva
PART A. Mark the correct answer.
[4]
1.1.
The system of equations
ax
+
by
+
cz
= 0
ax
+
cy
= ln
c
cx
+ (
a
+
b
)
xy
=
yz
(a) is linear in
{
x, y, z
}
and linear in
{
a, b
}
;
(b) is linear in
{
x, y, z
}
and linear in
{
b, c
}
;
(c) is nonlinear in
{
x, y, z
}
and linear in
{
a, b
}
;
(d) is nonlinear in
{
x, y, z
}
and linear in
{
b, c
}
;
(e) none of above.
Answer: c.
1.2.
The solution of the following system of equations
x
+
y
= 0
2
x

3
y
= 4
5
x
+ 6
y
=

2
(a) is
x
= 4 and
y
=

4;
(b) is
x
= 6 and
y
=

6;
(c) is
x
= 0 and
y
= 0;
(d) is
x
= 2 and
y
=

2;
(e) is none of the above.
Answer: e.
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AM 025b
Test 1 – January 31, 2008
2
Student #:
FOR INSTRUCTOR’S USE ONLY
1
2
3
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5
6
7
Total
4
8
8
10
10
10
10
60
[8]
2.1.
The following equation (
a
is a constant)
a
2
x

5 = 25
x
+
a
(a) has exactly one solution,
a
∈
R
;
(b) has infinitely many solutions regardless what
a
is;
(c) has no solution if
a
=

5;
(d) has a unique solution if
a
6
=
±
5.
Answer: d.
2.2.
If the augmented matrix of the system of linear equations is
1
0
3
0
6

3
0
1
2

3
0
8
0
0
1
0
0
3
0
0
0
0
1
0
then there (a) is a unique solution to this system;
(b) are infinitely many solutions with one free parameter;
(c) are infinitely many solutions with two free parameters;
(d) are infinitely many solutions with infinity many parameters;
(e) is no solution.
Answer: b.
2.3.
If
y
(
x
) =
ax
3
+
bx
2
+
cx
+
d
is a curve passing through the point
x
=

4
, y
= 3, then
(a) 4 =

3
x
3
+ 3
x
2

3
x
+
d
(b)

4 = 3
3
a
+ 3
2
b
+ 3
c
+
d
(c) 3 =

64
a
+ 16
b

4
c
+
d
(d) 4 =

3
3
a
+ 3
2
b

3
c
+
d
(e) none of the above.
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 Spring '11
 Gaussian Elimination, augmented matrix

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