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Math 20F.
Midterm Exam 2
March 8, 2006
Read each question carefully, and answer each question completely.
Show all of your work. No credit will be given for unsupported answers.
Write your solutions clearly and legibly. No credit will be given for illegible solutions.
1. (9 points) Consider the linear transformations
T
:
IR
3
→
IR
3
and
S
:
IR
3
→
IR
3
given
by
T
x
1
x
2
x
3
=
2
x
1

x
2
+ 3
x
3

x
1
+ 2
x
2

4
x
3
x
2
+ 3
x
3
,
S
x
1
x
2
x
3
=

x
1
2
x
2
3
x
3
(a) Find a matrix
A
associated to
T
and the matrix
B
associated to
S
. Show your
work.
(b) Is
T
onetoone? Is
T
onto? Justify your answer.
(c) Find the matrix of the composition
T
◦
S
:
IR
3
→
IR
3
. Justify your answer.
(a) Let
A
= [
T
(
e
1
)
, T
(
e
2
)
, T
(
e
3
)] and
B
= [
S
(
e
1
)
, S
(
e
2
)
, S
(
e
3
)]. Then,
A
=
2

1
3

1
2

4
0
1
3
,
B
=

1
0
0
0
2
0
0
0
3
.
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This note was uploaded on 04/23/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Math, Linear Algebra, Algebra

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