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Math 54, Quiz 1 Solutions
Sections 202/203
GSI Carter
1. For each of the following statements, write the word “true” or “false.”
(a)
xy
=
k
is a linear equation, where
x
and
y
are variables and
k
is a constant.
False, because the variables are being multiplied together.
(b) The following system of equations has at least one solution.
x
+
y

z
= 0
3
x
+ 2
y
+
z
= 0
x

2
y

2
x
= 0
7
x

y
+ 8
z
= 0
True, because every homogeneous system has at least the trivial solution.
2. Find all solutions to the following system of equations.
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Unformatted text preview: x + y + z = 5 2 xy + z = 10 4 x + y + 3 z = 20 The augmented matrix associated to this system can be row reduced as follows: ï£« ï£ 1 1 1 5 21 1 10 4 1 3 20 ï£¶ ï£¸ ï£« ï£ 1 1 1 53131 ï£¶ ï£¸ ï£« ï£ 1 1 1 5 1 1 3 ï£¶ ï£¸ Therefore the choice of z is arbitrary, and we have that y =z 3 and x = 5yz = 52 z 3 . 1...
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This note was uploaded on 02/20/2010 for the course AS a taught by Professor 11 during the Spring '10 term at Ã‰cole Normale SupÃ©rieure.
 Spring '10
 11

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