Name:
Tuesday section time:
Student ID:
Math 20F  Linear Algebra  Winter 2003
Quiz #4 — February 11
(Do not discuss the quiz with students who haven’t taken it yet – until 8:00pm.)
Let
v
1
=
2
1

1
,
v
2
=
2
0
2
, and
v
3
=

1

1
2
.
Answer the following questions. (As usual, be sure to justiﬁy your answers).
1. Are
v
1
,
v
2
,
v
3
linearly independent?
2. If not, show explicitly an example of how they are linearly dependent.
3. What is the dimension of
Span
(
v
1
,
v
2
,
v
3
)?
ANSWER: If they are linearly dependent, there is a nontrivial solution
to
22

1
10

1

12
2
x
=
0
.
We search for a nontrivial solution using row
reduction:



20
⇒



⇒
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 Winter '03
 BUSS
 Linear Algebra, Algebra, Vector Space, basis, nontrivial solution, Tuesday section time

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