MAS 3105
May 25, 2006
Quiz 3 and Key
Prof. S. Hudson
1) Find det(
A
), if
A
is 3x3 and it factors into
A
=
LU
=
1
0
0
l
21
1
0
l
31
l
32
1
u
11
u
12
u
13
0
u
22
u
23
0
0
u
33
2) Which of these are spanning sets of
R
3
? Justify your answers.
a)
{
(1
,
0
,
0)
T
,
(1
,
1
,
0)
T
,
(1
,
1
,
1)
T
,
(2
,
2
,
2)
T
}
b)
{
(1
,
1
,
0)
T
,
(2
,
2
,
0)
T
,
(1
,
1
,
1)
T
,
(2
,
2
,
2)
T
}
3) Choose ONE of these to prove (on the back is OK). Assume
A
and
B
are nxn matrices.
a) Show that if
AB
=
I
, then
BA
=
I
.
b) If
L
is a list of vectors in
V
, then span(
L
) is a subspace of
V
.
c) If
A
has two identical rows, then det (
A
) = 0 (use induction).
Bonus (5pt): Suppose
A
= [1 1 1; 2 2 2; 3 3 3] (notation as in MATLAB, etc). Without
doing any numerical work, predict the answer to
A
*
adj
A
=
Remarks + Answers:
The average was about 50/60. Problem 1) was pretty easy.
Problem 2 was harder, mainly because it came from Ch 3.2, not in HW3.
1) det(
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 Spring '09
 JULIANEDWARDS
 Linear Algebra, Vector Space, Det, Prof. S. Hudson, careful explanation method

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