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MATH 21
NOVEMBER 2, 2009
EXAM 1.2 — Solutions
Instructions
•
Please turn OFF all cell phones, iPods, etc.
.
•
There are 5 questions worth a total of 42 points. 100%=40 points.
•
Read all the questions before you begin. Answer the ones you ﬁnd easiest
ﬁrst
.
•
Please write
neatly
and show
all
your work.
•
No notes or books.
•
No calculators!
•
Take your time, and
check
your answers.
Good Luck!!!
NAME:
Zarathustra
Problem
Score
1
/14
2
/10
3
/6
4
/8
5
/4
Total
/40
1
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View Full Document MATH 21
EXAM 1
FALL 2009
(1)
Consider the matrix
M
=
1
1

1
0
1

1
0
3

2
1
2
2

2
1
5
2
1

4
3
3
.
a.
(4 pts) Write down the system of equations whose
augmented
matrix is
M
.
x
1
+
x
2

x
3
= 1

x
1
+ 3
x
3

2
x
4
= 1
2
x
1
+ 2
x
2

2
x
3
+
x
4
= 5
2
x
1
+
x
2

4
x
3
+ 3
x
4
= 3
b.
(6 pts) Find the reduced row echelon form of
M
.
M
∼
1
0

3
0

7
0
1
2
0
8
0
0
0
1
3
0
0
0
0
0
.
c.
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This note was uploaded on 03/16/2010 for the course ECON 11 taught by Professor Yk during the Spring '10 term at University of California, Santa Cruz.
 Spring '10
 yk

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