SAMPLE MIDTERM I
MATH 54 SEC.1, FALL 2009
80 POINTS, 80 MINUTES
Question 1, 9 pts
True or false? No justiFcation necessary. Correct answers carry 1
.
5 points,
incorrect answers carry 1
.
5 points penalty. However, you will not receive a negative total score.
T ±
If
x
∈
R
2
is not the zero vector, then each of its entries is nonzero.
T ±
The homogeneous system
A
x
=
0
has a nontrivial solution if and only if it has
at least one free variable.
T ±
If the equation
A
x
=
0
admits the trivial solution, then the columns of the matrix
A
are linearly independent.
T ±
The collection
{
[1
,
2]
T
,
[2
,
3]
T
,
[3
,
4]
T
}
is linearly independent.
T ±
In a linearly dependent collection of three vectors, each vector must be a linear combination
of the other two.
T ±
The column space of the matrix
A
is the set of all vectors which can be written as
A
x
,
for some vector
x
.
Question 2, 9 pts
True or false? No justiFcation necessary. Correct answers carry 1
.
5 points,
incorrect answers carry 1
.
5 points penalty. However, you will not receive a negative total score.
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 Fall '08
 Chorin
 Math, Linear Algebra, Vector Space, column space, negative total score

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