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Math 3013
Homework Set 7
Problems from
§
3.3 (pgs. 211212 of text): 1,3,5,7,9,11
Problems from
§
3.4 (pgs. 226229 of text): 1,5,7,16,20,26
1. (Problems 1,3,5,7,9,11 in
§
3.3) Find the coordinate vector of the given vector relative to the indicated
ordered basis.
(a) (Problem 3.3.1) [

1
,
1]
∈
R
2
, relative to ([0
,
1]
,
[1
,
0])
(b) (Problem 3.3.3) [4
,
6
,
2]
∈
R
3
, relative to ([2
,
0
,
0]
,
[0
,
1
,
1]
,
[0
,
0
,
1])
(c) (Problem 3.3.5) [3
,
13
,

1]
∈
R
3
, relative to ([1
,
3
,

2]
,
[4
,
1
,
3]
,
[

1
,
2
,
0])
(d) (Problem 3.3.7)
x
3
+
x
2

2
x
+ 4 in
P
3
, relative to
(
1
, x
2
, x, x
3
)
(e) (Problem 3.3.9)
x
+
x
4
in
P
4
, relative to
(
1
,
2
x

1
, x
3
+
x
4
,
2
x
3
, x
2
+ 2
)
(f) (Problem 3.3.11)
x
3

4
x
2
+ 3
x
+ 7 relative to
B
0
=
n
(
x

2)
3
,
(
x

2)
2
, x

2
,
1
o
2. Let
F
be the vector space of functions
f
:
R
→
R
. Determine whetther the following functions
T
are
linear transformations.
(a) (Problem 3.4.1)
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This homework help was uploaded on 04/22/2008 for the course MATH 3613 taught by Professor Binegar during the Spring '08 term at Oklahoma State.
 Spring '08
 BINEGAR
 Math, Algebra

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