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M340L FINAL EXAM 12:00
Your name:
SPRING, 2010
Dr. Schurle
Your UTEID:
Show all your work on these pages. Be organized and neat. Your work should be your
own; there should be no talking, reading notes, checking laptops, using cellphones, .
. . .
THE EXAM HAS 14 PROBLEMS.
1. (6 points) Use parametric vector form to describe all solutions of the system
A
x
=
b
,
where
A
and
b
are given below. DO NOT USE A CALCULATOR!! SHOW ALL
YOUR WORK STEP BY STEP!!
A
=
1
2
0
3
5
2
4
1 10 16
3
6

1
5
9

1

2
2
5
7
and
b
=
7
22
13
9
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View Full Document YOUR SCORE:
/100
2. (7 points) Are the columns of the following matrix linearly independent? Show all your
work and justify your answers.
1 1
2 1
2 4
5 3
3 1
4 4

1 3

3 7
3. (7 points) Find the inverse of
A
=
"
3 4
2 2
#
and use it to solve 2
AX

B
=
C
for
X
,
where
B
=
"
2 1 3
1 1 0
#
and
C
=
"
6 4 2
0 2 2
#
.
4. (9 points) Suppose
T
is a linear transformation from
R
4
to
R
2
for which
T
a
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This note was uploaded on 06/15/2011 for the course M 340L taught by Professor Pavlovic during the Fall '08 term at University of Texas at Austin.
 Fall '08
 PAVLOVIC
 Linear Algebra, Algebra

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