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Math 20F
Test
1
100 points
January 28, 2009

Notation:
All scalars and matrix entries are in the set
R
of real numbers.
Points:
(1)
,
(2)
12 pts each
(3A),(3B),(3C)
,
(4)
15 pts each
(3D)
10 pts
(3E)
6 pts
Directions:
Show all work and justify all answers, except in problems (1) and (2).

(1)
Let
S = {
v
1
, . . . ,
v
n
}
be a set of
n
vectors in
R
m
.
Complete the following
sentences in such a way as to provide precise, explicit definitions:
(A)
The set
S
is called
linearly dependent
if ___________________________.
(B)
The
span
of
S
is defined to be the set
______________________________.

(2)
Let
T :
R
n
a
R
m
be a function (i.e., a transformation).
Complete the following
sentences in such a way as to provide precise, explicit definitions:
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This note was uploaded on 03/17/2011 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Linear Algebra, Algebra, Real Numbers, Scalar

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