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Math 20F  Linear Algebra  Winter 2003
Quiz #
3
1
2
— February 4
Answers
1. Let
S
=
n‡
x
y
·
∈
R
2
:
x
2
≥
y
o
.
Is
S
a subspace of
R
2
?. Prove your
answer.
Don’t be frightened by the word “Prove”. It means the same as
“Justify” or “Show your evidence”. For this particular problem,
showing a counterexample to a closure property is enough.
ANSWER: We show that
S
is not closed under vector addition. For
example,
(
1
1
)
and
(

1
1
)
are in
S
. However
±
1
1
¶
+
±

1
1
¶
=
±
0
2
¶
/
∈
S.
2. Let
v
1
=
1
2
3
and
v
2
=
4
5
6
.I
s
{
v
1
,
v
2
}
a spanning set for
R
3
.
If not, give an example of a
x
∈
R
which is not in
span
(
v
1
,
v
2
).
ANSWER: We need to determine whether there is a vector (
abc
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This homework help was uploaded on 01/23/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Linear Algebra, Algebra

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