NAME:
CODEWORD:
MAS 3114
—
MIDTERM EXAM
—
May 28, 2004
Instructions:
•
Total possible points = 87.
•
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. Only scientific calculators are allowed.
•
Set out your work properly.
Explain your reasoning clearly and make your
answer clear.
1.
[4 pts]
Complete the following.
DEFINITION
. If
v
1
,
v
2
, . . . ,
v
p
are in
R
n
, then the set of
.......................................
...........................
of
v
1
,
v
2
, . . . ,
v
p
is denoted by Span
{
v
1
,
v
2
, . . . ,
v
p
}
and is called
the
subset of
R
n
.........................
(or
generated
)
by v
1
,
v
2
, . . . ,
v
k
. That is, the
Span
{
v
1
,
v
2
, . . . ,
v
p
}
is the collection of all vectors that can be written in the form
.........................................................................
with
....................................
scalars.
2.
[6 + 2 = 8 pts] Let
A
=
1

1
7
1

2
4
1
3
1
and
b
=
8
3
10
.
Denote the columns of
A
by
a
1
,
a
2
,
a
3
(a) Determine whether
b
is in Span
{
a
1
,
a
2
,
a
3
}
.
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 Fall '08
 Olson
 Linear Algebra, Vector Space, .........

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