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51
WeBWorK assignment due : 04/06/2016 at 03:00am EDT.
1.
(1 pt) Let
W
1
be the set:
?
?
1
0
0
?
?
,
?
?
1
1
0
?
?
,
?
?
1
1
1
?
?
.
Determine if
W
1
is a basis for
R
3
and check the correct an
swer(s) below.
•
A.
W
1
is a basis.
•
B.
W
1
is not a basis because it does not span
R
3
.
•
C.
W
1
is not a basis because it is linearly dependent.
Let
W
2
be the set:
?
?
1
0
1
?
?
,
?
?
0
0
0
?
?
,
?
?
0
1
0
?
?
.
Determine if
W
2
is a basis for
R
3
and check the correct an
swer(s) below.
•
A.
W
2
is not a basis because it is linearly dependent.
•
B.
W
2
is a basis.
•
C.
W
2
is not a basis because it does not span
R
3
.
2.
(1 pt) Let
W
1
be the set:
?
?
1
3
0
?
?
,
?
?
2
9
0
?
?
,
?
?
0
0
0
?
?
,
?
?
0
3
5
?
?
.
Determine if
W
1
is a basis for
R
3
and check the correct an
swer(s) below.
•
A.
W
1
is not a basis because it is linearly dependent.
•
B.
W
1
is a basis.
•
C.
W
1
is not a basis because it does not span
R
3
.
Let
W
2
be the set:
?
?
2
3
0
?
?
,
?
?
6
1
5
?
?
.
Determine if
W
2
is a basis for
R
3
and check the correct an
swer(s) below.
•
A.
W
2
is not a basis because it is linearly dependent.
•
B.
W
2
is a basis.
•
C.
W
2
is not a basis because it does not span
R
3
.
3.
(1 pt) Find the coordinate vector of
x
=
?
?

2
5

4
?
?
with re
spect to the basis
B
=
?
?
?
?
?
1
2
4
?
?
,
?
?
0
1

2
?
?
,
?
?
0
0
1
?
?
?
?
?
or
R
3
.
[
x
]
B
=
?
?
?
?
4.
(1 pt) Find a basis of the subspace of
R
4
consisiting of all
vectors of the form
?
?
?
?
x
1

2
x
1
+
x
2
7
x
1

3
x
2
4
x
1
+
8
x
2
?
?
?
?
.
?
?
?
?
?
?
?
?
,
?
?
?
?
?
?
?
?
.
5.
(1 pt) Find a basis of the subspace of
R
4
de?ned by the
equation

6
x
1

3
x
2

8
x
3

7
x
4
=
0.
?
?
?
?
?
?
?
?
,
?
?
?
?
?
?
?
?
,
?
?
?
?
?
?
?
?
.
6.
(1 pt) Find a set of vectors u, v in
R
4
that spans the solu
tion set of the equations:
x

y

3
w
=
0
3
x
+
2
y
+
z

3
w
=
0
u
=
?
?
?
?
?
?
?
?
,
v
=
?
?
?
?
?
?
?
?
.
7.
(1 pt) Let
A
=
±
1
1
1
1
2
2
2
2
²
.
Describe all solutions of
Ax
=
0.
x
=
x
2
?
?
?
?
?
?
?
?
+
x
3
?
?
?
?
?
?
?
?
+
x
4
?
?
?
?
?
?
?
?
8.
(1 pt)
Let
A
=
±
2
9
2
7
2
3
²
.
De?ne the linear transformation
T
:
R
3
?
R
2
as
T
(
x
) =
Ax
.
1
Answer