Linear Algebra 1600a Midterm
7:0010:00 pm
October 30, 2009
Last Name
First Name
Student ID
CIRCLE LECTURE AND LAB SECTIONS:
1
2
3
4 + 5
6
7
8
Σ
19
8
9
9
15
6
4
70
This exam has 11 problems on 8 pages.
LECTURE:
001 MWF 8:30
002 MWF 10:30
LAB:
003 W 9:30
004 Th 2:30
005 Th 11:30
006 W 3:30
007 Th 12:30
008 W 11:30
NO CALCULATORS, NOTES OR OTHER AIDS.
1.
For each of the following, circle
T
if the statement is always true and circle
F
if it can be false.
(16 pts)
If you are unsure, leave blank.
Wrong answers will receive

2 marks
.
(a)
If
A
is a 3
×
4 matrix and
b
is in
R
3
,
then the system
A
x
=
b
has infinitely many solutions.
T
F
(b)
If
A
is an invertible matrix, then the system
A
x
=
b
has exactly one solution for every
b
.
T
F
(c)
For any
m
×
n
matrix
A
, the set of solutions to
A
x
=
0
is a subspace of
R
n
.
T
F
(d)
Every set of four vectors in
R
3
is linearly dependent.
T
F
(e)
If
A
is a square matrix with two identical columns, then det(
A
) = 0.
T
F
(f)
If
A
is skewsymmetric, then
A
T
is symmetric.
T
F
(g)
λ
= 1 is an eigenvalue of every square matrix
A
.
T
F
(h)
If
u
and
v
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 Spring '11
 Linear Algebra, Vector Space, pts

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