Christian Searing
Math4A01F14BIGELOW
Assignment hw2 due 10/20/2014 at 10:15pm PDT
1.
(1 pt) Let
v
1
=
4
1
3
,
v
2
=
16
5
12
,
v
3
=
23
7
18
and
w
=
6
0
8
.
1
.
Is
w
in
{
v
1
,
v
2
,
v
3
}
? Type ”yes” or ”no”.
2
.
How many vectors are in
{
v
1
,
v
2
,
v
3
}
?
Enter ”inf” if the
answer is infinitely many.
3
.
How many vectors are in
Span
{
v
1
,
v
2
,
v
3
}
?
Enter ”inf” if
the answer is infinitely many.
4
.
Is
w
in the subspace spanned by
{
v
1
,
v
2
,
v
3
}
?
Type ”yes”
or ”no”.
Correct Answers:
•
NO
•
3
•
INF
•
YES
2.
(1 pt) Let
W
be the set of all vectors of the form:
2b+4c
b
c
. Find vectors
u
and
v
such that
W
=
Span
{
u
,
v
}
.
u
=
,
v
=
Correct Answers:
•
\(\displaystyle\left.\begin{array}{c}
\mbox{2} \cr
\mbox{1} \cr
\mbox{0} \cr
\end{array}\right.\) ,\(\displaystyle\left.\begin{array}{c}
\mbox{4} \cr
\mbox{0} \cr
\mbox{1} \cr
\end{array}\right.\)
3.
(1 pt) If
Au
=
3
4
4
and
Av
=
4
2
1
, then
A
(

3
u
+
3
v
) =
Correct Answers:
•
21
•
6
•
15
4.
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 Spring '13
 SCHARLEMANN
 Math, Vector Space, Euclidean vector, Christian Searing