Write a regular expression that matches prices, i$.$e$.,$ a $ symbol, followed by at least one digit. If there

is a decimal point, there must be at least one digit before it$,$ and exactly two digits after it$.$ There are no

commas. Draw the corresponding finite automaton.

Improve your regex such that it accepts $$0$ and $$0\mathrm{.}00$ but rejects all other inputs that start with $$0$ and

continue with other symbols, e$.$g$.,$ $$00,$$$01,$$$00\mathrm{.}00.$ Draw the corresponding finite automaton.

Improve your regex such that it also accepts commas in the thousands, millions places, etc. For example,

$$1,000,$$$1,000,000\mathrm{.}00$ are accepted.

A matrix M has $7$ rows and $3$ columns.

$($a$)$ what is its dimension?

$($b$)$ what is the dimension of M$^($TT$),$ the transpose of M $?$

$($c$)$ what is the dimension of M$^($TT$)$M $?$

$($d$)$ what is the dimension of MM$^($TT$)?$