MAS 3114
—
Final Exam
—
December 16, 1994
Instructions:
•
There are 13 problems giving a total of 210 points (this includes 10 bonus
points). Answer all these questions.
•
In this test boldface is used to indicate a vector; eg.
v
is a vector but
x
is a
scalar. In your work distinguish between vectors and scalars by underlining vectors;
eg.
v
is a vector but
x
is a scalar.
•
Show all necessary working. Calculators are not
allowed.
•
Set out your work properly.
Explain your reasoning clearly and make your
answer clear.
•
Answer 4(i), (ii) and part of 13(iii) on the test paper. Answer the remainder on
your own paper. Write on ONE side of your paper.
Leave blank.
1.
2.
3.
4.
5.
6.
10.
7.
11.
8.
12.
9.
13.
[1 point]
Name:
[1 point]
Did you write on ONE side of your paper ?
1
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2
1.
[4 + 10 = 14 points]
(i)
Let
v
1
,
v
2
, . . . ,
v
p
be vectors in
R
n
.
Define the set denoted by Span
{
v
1
,
v
2
, . . . ,
v
p
}
.
(ii)
Let
v
1
=
1
2

1

2
,
v
2
=
1
0
2
0
,
v
3
=
3
2
3

2
.
Determine if
v
3
is in the Span
{
v
1
,
v
2
}
.
2.
[4 + 18 = 22 points]
(i)
Define what it means for a set
{
v
1
,
v
2
, . . . ,
v
k
}
of vectors in
R
n
to be
linearly
independent
.
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 Fall '08
 Olson
 Linear Algebra, Vector Space, linear transformation

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