SAMPLE FINAL EXAM
MATH 54 SEC.1, FALL 2009
90 POINTS, 180 MINUTES
Question 1, 18 pts
True or false? No justification necessary. Correct answers carry 1
.
5 points,
incorrect answers carry 1
.
5 points penalty. However, you will not receive a negative total score on
any group of 6 questions.
T
F
If an augmented matrix [
A
b
] is transformed into [
C
d
] by elementary row operations,
then the systems
a
x
=
b
and
C
x
=
d
have exactly the same solution sets.
T
F
If
{
u
,
v
,
w
}
is linearly independent, then
u
,
v
and
w
are not in
R
2
.
T
F
For any matrix
A
, det(

A
) =

det(
A
).
T
F
For any square matrix
A
, det(
A
T
A
)
≥
0.
T
F
If
u
and
v
are in
R
2
and det[
u v
] = 10, then the area of the triangle in the plane
with vertices at
0
,
u
and
v
is 10.
T
F
If two row exchanges are made in succession, then the new determinant equals the
old determinant.
T
F
If
λ
+ 5 is a factor of the characteristic polynomial of
A
, then 5 is an eigenvalue of
A
.
T
F
Eigenvalues of a matrix must be nonzero scalars.
T
F
A square matrix
A
is invertible if and only if there is a coordinate system in which
the linear transformation
x
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 Fall '08
 Chorin
 Math, Linear Algebra, square matrix

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