Math 152, Spring 2010
Assignment #4
Notes:
•
Each question is worth 5 marks.
•
Due in class: Monday, February 1 for MWF sections; Tuesday, February
2 for TTh sections.
•
Solutions will be posted Tuesday, February 2 in the afternoon.
•
No late assignments will be accepted.
1. Consider the intersection between the following two planes given in
parametric form:
P
1
:
x
= [2
,
4
,
3] +
s
1
[1
,
2
,
1] +
s
2
[2
,
5
,
4]
P
2
:
x
= [1
,
0
,

5] +
t
1
[3
,
8
,
7] +
t
2
[2
,
1
,

5]
Find the intersection as a line in parametric form.
2. Reduce the matrix

1
2
0
1
4
1

2
0
0

1
2

6
2
4
0
to reduced row echelon form and determine the rank of the matrix.
(a) Do this question by hand.
(b) Write by hand the MATLAB commands that would enter the
matrix above and compute its reduced row echelon form.
3. Consider the set of vectors:
a
1
= [1
,
2
,
3
,

1]
,
a
2
= [

2
,

3
,

5
,
1]
,
a
3
= [1
,
4
,
5
,

3]
,
a
4
= [

1
,

3
,

4
,
2]
,
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(a) Find all possible
s
1
, s
2
, s
3
, s
4
such that
[4
,
1
,
3
,
5] =
s
1
a
1
+
s
2
a
2
+
s
3
a
3
+
s
4
a
4
.
(b) Show that the vectors
a
1
,
a
2
,
a
3
,
a
4
are linearly dependent by ex
pressing
a
3
and
a
4
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 Spring '08
 Caddmen
 Math, Linear Algebra, Vector Space, Row echelon form

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