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ma253
,Fa
l
l
2007
— Problem Set
2
This problem set covers systems of linear equations and Gaussian elimination,
basics of column vectors and
R
m
, and a little bit about linear spaces. As usual,
solve all the problems, then write up and turn in those marked with an asterisk.
This assignment is due on
Wednesday, September 26
.
1.
Problems from the textbook:
a. Section
1
.
1
, problem *
46
b. Section
1
.
2
, problem
50
,*
53
.
c. Section
1
.
3
, problems
1
,
2
,*
4
,
13
,
15
,
17
,*
19
,
20
,*
21
,*
22
,*
24
,
38
,
46
,
*
47
,*
48
.
*2.
Decide whether each of these sets, with the natural operations, is a linear space.
(All you need to do is to decide whether the conditions in
4
.
1
.
1
are all satis±ed.)
You need not justify your answer.
a. The space of all
n
-entry column vectors.
b. The space of all
m
-entry row vectors.
c. The space of all polynomials of degree
5
.
d. The space of all polynomials of degree at most

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