Math 3013
Homework Set 5
Problems from
§
2.1 (pgs. 134136 of text): 1,3,11,12,13,16,23
Problems from
§
2.2 (pgs. 140141 of text): 1,3,5,7,11,12
Problems from
§
2.3 (pgs. 152154 of text): 1,2,3,4,5,7,13,15,19,29
Math 3013
Problem Set 5
Problems from
§
2.1 (pgs. 134136 of text): 1,3,11,12,13,16,23
Problems from
§
2.2 (pgs. 140141 of text): 1,3,5,7,11
Problems from
§
2.3 (pgs. 152154 of text): 1,2,3,4,5,7,13,15,19,29
1. (Problem 2.1.1 in text). Give a geometric criterion for a set of two distinct nonzero vectors in
R
2
to be
dependent.
2. (Problem 2.1.3 in text). Give a geometric criterion for a set of two distinct nonzero vectors in
R
3
to be
dependent.
3. (Problem 2.1.11 in text). Find a basis for the subspace spanned by the vectors [1
,
2
,
1
,
1], [2
,
1
,
0
,

1],
[

1
,
4
,
3
,
8], [0
,
3
,
2
,
5]
∈
R
4
.
4. (Problem 2.1.12 in text). Find a basis for the column space of the matrix
A
=
2
3
1
5
2
1
1
7
2
6

2
0
5. (Problem 2.1.13 in text). Find a basis for the row space of the matrix
A
=
1
3
5
7
2
0
4
2
3
2
8
7
6. (Problems 2.1.16 and 2.1.23 in text). Determine whether the following sets of vectors are dependent or
independent.
(a)
{
[1
,
3]
,
[

2
,

6]
}
in
R
2
.
(b)
{
[1
,

4
,
3]
,
[3
,

11
,
2]
,
[1
,

3
,

4]
}
in
R
3
.
7. (Problems 2.2.1, 2.2.3, and 2.2.5 in text). For each of the following matrices find the rank of the matrix,
a basis for its row space, a basis for its column space, and a basis for its null space.
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 Spring '08
 BINEGAR
 Math, Linear Algebra, Algebra

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