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110.201 Linear Algebra
3rd Quiz
March 24, 2005
Notation.
•
P
n
= space of polynomials, with real coeﬃcients, of degree at most
n
.
•
R
m
×
n
= space of
m
by
n
real matrices.
Problem 1
Determine whether the following spaces are isomorphic. In case
they are isomorphic, deﬁne an isomorphism relating them. Justify your answer.
1.
R
2
and
R
4
2.
P
5
and
R
5
3.
R
2
×
3
and
R
6
4.
P
5
and
R
2
×
3
5.
R
2
×
k
and
C
k
, for
k
∈
N
Problem 2
Let
V
=
C
1
([0
,
1]) be the set of continuously diﬀerentiable func
tions on the closed interval [0
,
1].
V
is a real linear space with respect to the
operations of pointwise addition of functions and scalar multiplication.
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 Spring '05
 CONSANI
 Linear Algebra, Algebra, Polynomials, Matrices

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