Math 152, Spring 2011
Assignment #5
Notes:
•
Each question is worth 5 marks.
•
Due in class: Monday, February 7 for MWF sections; Tuesday, Febru
ary 8 for TTh sections.
•
Solutions will be posted Tuesday, February 8 in the afternoon.
•
No late assignments will be accepted.
(1)
(a) (1 mark) Find the equation form of the plane
P
with normal vector
b
= [1
,
0
,

1] and passing through the point
q
= [0
,

1
,
0].
(b) (1 mark) Find the equation form of the line
L
that is perpendicular
to the plane
Q
with equation

x
+3
y
+2
z
= 1 and passing through
the origin.
(c) (3 marks) Use Gaussian elimination to determine the intersection
between the plane
P
and the the line
L
.
(2)
(a) (2 marks) Use Gaussian elimination to ﬁnd the set of solutions
to the following homogeneous system. Present your answer in
parametric form.
x
1

x
2
+
x
4
= 0
x
1
+ 4
x
2

x
3
+
x
4
= 0
2
x
1

x
2
+
x
3
+ 3
x
4
= 0
3
x
1
+ 3
x
2
+ 4
x
4
= 0
.
(b) (1 mark) Consider the following inhomogeneous linear system:
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 Spring '08
 Caddmen
 Math, Linear Algebra, Gaussian Elimination, Vector Space

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