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
. Is
{
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 (
a b c
)
T
so
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 Winter '03
 BUSS
 Linear Algebra, Algebra, Vector Space

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