AMS 510.01 Fall 2008, Midterm #1
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( +
/15 bonus)
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•
Write all solutions on this paper; extra sheets are available if needed.
•
Explain your answers and show all work. For all problems except question 1 (true and false),
correct answers with incomplete work will not be given full points.
•
Calculators may
not
be used.
•
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1. Indicate whether each of the following statements is true or false.
n
should be taken as any
constant
positive integer. (2 points each).
(a) The set of all rational numbers is closed with respect to both addition and multiplication.
(b) The dimension of the vector space of all vectors of the form (
a, b,
0) is three. That is:
V
=
{
x
:
x
= (
a, b,
0)
,
∀
a, b
∈
R
} →
dim(
V
) = 3
(c)
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
= 3
(d) The set of all matrices of the form:
a
0
0
b
where
a, b
∈
C
, forms a vector space.
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 Fall '08
 Feinberg,E
 Linear Algebra, Applied Mathematics, Vector Space, 0 m, Square Matrices, bT Cx

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