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Math 225
Spring 2008
Rosen
Assignment 17
1.
Show that
{
}
,
n
R
R
is a Normed Linear Space.
2.
Show that
[
]
{
}
,
,
p
C a b
with
1
p
=
and
p
=
are Normed Linear Spaces.
3.
For
n n
A
R
R
R
let
(
29
,
1
max
n
i j
i
j
N A
a
=
=
(i.e. the maximum absolute row sum of A)
and let
:
n
n
F R
R
R
be given by
(
29
F x
Ax
=
r
r
for
n
x
R
R
r
,
Show that
(
29
(
29
(
29
F x
F y
N A x
y
R
R


r
r
r
r
for
,
n
x y
R
R
r r
.
Conclude that
:
n
n
F R
R
R
is continuous from
{
}
,
n
R
R
into
{
}
,
n
R
R
.
4.
For
[
]
1
,
x
C a b
R
let
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Unformatted text preview: [ ] ( 29 [ ] ( 29 1 , , max max C t a b t a b x x x x t x t R & = + = + . Show that [ ] { } 1 1 , , C C a b is a Normed Linear Space. Let [ ] [ ] 1 : , , F C a b C a b R given by ( 29 F x xR = for [ ] 1 , x C a b R is continuous from [ ] { } 1 1 , , C C a b into [ ] { } , , C a b R...
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This note was uploaded on 03/31/2008 for the course MATH 225 taught by Professor Guralnick during the Spring '07 term at USC.
 Spring '07
 Guralnick
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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