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Section Time:
Math 20F.
Final Exam
December 7, 2005
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. Consider the matrix
A
=
1

1
0
2
0
1
0
1

1
.
(a) (4 Pts.) Find the inverse of the matrix
A
.
(b) (2 Pts.) Use the part (1a) to solve the system
A
x
=
b
, with
b
=
1

1
3
.
#
Score
1
2
3
4
5
6
7
8
9
Σ
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View Full Document 2. Let
T
:
IR
2
→
IR
3
be a linear transformation given by
T
(
x
1
, x
2
) =
x
1

2
x
2
3
x
1
+
x
2
x
2
.
(a) (2 Pts.) Find the matrix
A
associated to the linear transformation
T
using the
standard bases in
IR
3
and
IR
2
.
(b) (2 Pts.) Is
T
onetoone? Justify your answer.
(c) (2 Pts.) Is
T
onto? Justify your answer.
3. Let
B
=
{
b
1
,
b
2
,
b
3
}
and
C
=
{
c
1
,
c
2
,
c
3
}
be two bases of
IR
3
, and suppose that
c
1
=
b
1

2
b
2
+
b
3
,
c
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This note was uploaded on 04/07/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Math, Algebra

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