2015
年
3
月
17
日
UW Common Math 308 Section 4.1
1/21
Current Score :
29 / 30
Due :
Tuesday, February 17 2015 11:00 PM PST
1.
1/1 points |
Previous Answers
HoltLinAlg1 4.1.003.
Determine if the described set is a subspace. Assume
a
and
b
are real numbers.
The subset of
consisting of vectors of the form
where
If so, give a proof. If not, explain why not.
R
2
,
a
b
a
+
b
= 1.
The set is a subspace.
The set is not a subspace.
(No Response)
Key:
Answers will vary.
This answer has not been graded yet.
Solution or Explanation
Not a subspace, because
and thus
0
is not in this set.
UW Common Math 308 Section 4.1 (Homework)
YIFANG CHEN
Math 308, section N, Winter 2015
Instructor: Graham J Clenaghan TA
WebAssign
The due date for this assignment is past.
Your work can be viewed below, but no changes can be made.
0 + 0
≠
1,

2015
年
3
月
17
日
UW Common Math 308 Section 4.1
2/21
2.
1/1 points |
Previous Answers
HoltLinAlg1 4.1.006.
Determine if the described set is a subspace. Assume
a
and
b
are real numbers.
The subset of
consisting of vectors of the form
If so, give a proof. If not, explain why not.
R
4
.
a
a
+
3
a
−
9
b
The set is a subspace.
The set is not a subspace.
(No Response)
Key:
Answers will vary.
This answer has not been graded yet.
Solution or Explanation
Let
S
be the set of vectors of the form
Then
S
= span
and hence
S
is a subspace.
b
b
.
a
a
+
b
3
a
−
b
9
b
,
,
1
1
3
0
0
1
−1
9

2015
年
3
月
17
日
UW Common Math 308 Section 4.1
3/21
3.
0/1 points |
Previous Answers
HoltLinAlg1 4.1.007.
Determine if the described set is a subspace.
The subset of
consisting of vectors of the form
where
a
and
b
are integers.
If so, give a proof. If not, explain why not.
R
2
,
a
b
The set is a subspace.
The set is not a subspace.
(No Response)
Key:
Answers will vary.
This answer has not been graded yet.
Solution or Explanation
Not a subspace. Let
and
Then
u
belongs to the set, but
does
not.
r
=
1
2
u
=
.
1
0
r
u
=
1/2
0

2015
年
3
月
17
日
UW Common Math 308 Section 4.1
4/21
4.
1/1 points |
Previous Answers
HoltLinAlg1 4.1.009.
Determine if the described set is a subspace. Assume
a
,
b
, and
c
are real numbers.
The subset of
consisting of vectors of the form
where
If so, give a proof. If not, explain why not.
R
3
,
a
b
c
abc
= 0.
The set is a subspace.
The set is not a subspace.
(No Response)
Key:
Answers will vary.
This answer has not been graded yet.
Solution or Explanation
Not a subspace. Let
and
Then both
u
and
v
belong to the subset, but
does not, since
u
=
1
0
0
v
=
.
0
1
1
u
+
v
=
1
1
1
1(1)(1) = 1
≠
0.

2015
年
3
月
17
日
UW Common Math 308 Section 4.1