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ma253
,Fa
l
l
2007
— Problem Set
8
Bases, dimension, coordinatization, and the matrix of a linear transformation:
all neat stuff. This is due on
Wednesday, November 14
.
1.
Problems from the textbook:
a. Section
3
.
3
, problems
43
,
44
,
47
,*
62
,*
63
,*
64
.
b. Section
3
.
4
, problems *
2
,*
4
,*
8
,*
14
,*
18
,*
20
,*
24
,*
30
.
c. Section
4
.
2
, problems
63
,*
70
,*
72
,
78
,*
80
.
d. Section
4
.
3
, problems
1
,*
3
,*
4
,*
20
,*
22
,*
28
,*
32
.
*2.
Suppose
{
~
v
1
,...,
~
v
k
}
is a set of vectors that spans a vector space
V
,andthat
T
:
V

→
W
is a linear transformation that is onto. Show that the set
{
T
(
~
v
1
)
,...,T
(
~
v
k
)
}
spans
W
.
*3.
Suppose
{
~
v
1
,...,
~
v
k
}
is a linearly independent set of vectors in a linear space
V
,
and that
T
:
V

→
W
is a linear transformation that is onetoone. Show that the
set
{
T
(
~
v
1
)
,...,T
(
~
v
k
)
}
is a linearly independent subset of
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 Fall '07
 GHITZA
 Linear Algebra, Algebra

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