$($a$)$ Enter the

matrices$$C$$and$$I$$into

MATLAB.

$>>$C $=[0\mathrm{.}250\mathrm{.}150\mathrm{.}250\mathrm{.}180\mathrm{.}20$;

$0\mathrm{.}150\mathrm{.}280\mathrm{.}180\mathrm{.}170\mathrm{.}05$;

$0\mathrm{.}220\mathrm{.}190\mathrm{.}220\mathrm{.}220\mathrm{.}10$;

$0\mathrm{.}200\mathrm{.}150\mathrm{.}200\mathrm{.}280\mathrm{.}15$;

$0\mathrm{.}180\mathrm{.}230\mathrm{.}150\mathrm{.}150\mathrm{.}50]$

$>>$I $=$ eye$(5)$

Note that the command "eye$($n$)"$ creates an n x n matrix with $1\text{'}$s

on the diagonal and $0\text{'}$s elsewhere.

$$

$($b$)$ Use MATLAB to row reduce the

augmented matrix $[$C $-$

I$|$d$]$ and write down

the general solution to$($C $-$

I$)$p$=0.$

$$

$($c$)$ What are the highest and the lowest

priced commodities in Matrixville?$$ List the inhabitants of

this charming town in order of increasing income.$$ If our

friend Bob makes $$40,000$ per year, what are the incomes for the

rest of the inhabitants?$$ With all the moonshine that Bob

drinks, do you think he will live long enough to enjoy his good

life?