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Math 3353
Matlab Assignment 3  Due 11/02/09
T. Hagstrom
1. Consider the following transformation from
P
6
→
P
6
:
T
(
p
) =

d
2
p
dx
2
+ 2
p
i.
Verify (on paper!) that
T
is a linear transformation.
ii.
Using the monomial basis for
P
6
,
{
1
, x, x
2
, . . . , x
6
}
, build, in Matlab, the matrix representing
T
.
Use the Matlab command
null
to verify that the matrix is invertible.
iii.
Use Matlab and the matrix constructed above to ﬁnd
p
∈
P
6
satisfying:

d
2
p
dx
2
+ 2
p
=
x
6
+
x
4
+
x
2

3
x
Write out the polynomial,
p
, that you compute.
2. Consider an agestructured population model based on exisiting data for the US. We break the
population into groups of 5 years. That is,
x
k
= population aged 5
k

5 to 5
k

1 years
We set
x
21
to be the total number of people aged 100 or more. In a given year the population changes
by the following processes:
i.
Births 
x
1
is increased by the sum of the birth rates for each group mulitplied by the population
in each group:
X
k
b
k
x
k
ii.
Deaths 
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This note was uploaded on 11/11/2009 for the course MATH 3353 taught by Professor Thomashagstrom during the Spring '09 term at SMU.
 Spring '09
 ThomasHagstrom
 Linear Algebra, Algebra, matlab

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