Given

$0\mathrm{.}30\mathrm{.}30\mathrm{.}4$

P$=0\mathrm{.}60\mathrm{.}10\mathrm{.}3$

$0\mathrm{.}20\mathrm{.}70\mathrm{.}1$

Using the Excel, find the following. Hint: You may want to use the functions MMULT and

MINVERSE. $($Alternatively$,$ you can do this in Python. Provide a file with the code and

answers.$)$

a$)$ P

$2$

b$)$ P

$16$

c$)($I$-$P$)$ where I is a $3$x$3$ identity matrix

d$)$ Modify the answer above by making the last column all $1$s$.$ Call this matrix A$.$

e$)$ Find A

$-1$

$.$

f$)$ Let b be a $(1$x$3)$ row vector $[001].$ Compute bA$-1$

$.$

g$)$ Compare the answer to f$)$ to last row of A

$-1$

$.$ What do you notice?

h$)$ Compare the answer to f$)$ to any row in the answer to b$).$ What do you notice?