Math 3013
Homework Set 1
Problems from
§
1.1 (pg. 15  17 of text): 1,9,31,35
Problems from
§
1.2 (pg. 31  33 of text): 1,3,22,23,25,27,33
Problems from
§
1.3 (pg. 46  48 of text): 1,3,7,9,11,13,14,19,21
1. (Problem 1.1.1 and 1.1.3 in text). Let
v
= [2
,

1] and
w
= [

2
,

3]. Compute
v
+
w
,
v

w
and then
draw coordinate axes and sketch, using your answers the vectors
v
,
w
,
v
+
w
, and
v

w
.
(a)
v
= [2
,

1],
w
= [

3
,

2].
(b)
v
=
i
+ 3
j
+ 2
k
,
i
+ 3
j
+ 4
k
, where
i
= [1
,
0
,
0],
j
= [0
,
1
,
0],
k
= [0
,
0
,
1] are the standard basis vectors of
R
3
.
2. (Problem 1.1.9 in text). Let
u
= [1
,
2
,
1
,
0],
v
= [

2
,
0
,
1
,
6] and
w
= [3
,

5
,
1
,

2].
Compute
u

2
v
+4
w
.
3.
(Problem 1.1.31 in text).
Find the vector which, when translated, represents geometrically an arrow
reaching from the point (

1
,
3) to the point (4
,
2) in
R
2
.
4. (Problems 1.2.1 and 1.2.3 in text). Let
u
= [

1
,
3
,
4] and
v
= [2
,
1
,

1]. Compute

u
and
v
+
u
.
5. (Problem 1.2.22 in text). Compute the angle between [1
,

1
,
2
,
3
,
0
,
4] and [7
,
0
,
1
,
3
,
2
,
4] in
R
6
.
6. (Problem 1.2.23 in text) Prove that (2
,
0
,
4), (4
,
1
,

1) and (6
,
7
,
7) are the vertices of a right triangle in
R
3
.
7. (Problems 1.2.25 and 1.2.27 in text). Classify the vectors as parallel, perpendicular, or neither.
If they
are parallel, state whether they have the same or opposite directions.
(a) [

1
,
4] and [8
,
2].
(b) [3
,
2
,
1] and [

9
,

6
,

3].
8. (Problem 1.2.22 in text). Find the distance between the points (2
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 Spring '08
 BINEGAR
 Math, Linear Algebra, Algebra, Vector Motors, Standard basis

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