$1.[40$ points total$]$ Consider the following snapshot of a system:

Answer the following questions using the banker's algorithm:

a$.[10$ points$]$ Show the content of the matrix Need below.

b$.[10$ points$]$ Show that the system in a safe state by listing the order in which processes can be executed without producing a deadlock. Show your work above if you want any partial credit.

c$.[10$ points$]$ If a request from process $\backslash ($ P$\_\{0\}\backslash )$ arrives for $\backslash ((2,2,0,0)\backslash ),$ can the request be granted immediately? If yes, then list the order in which processes can be executed without producing a deadlock. Otherwise $[20]$ show the order in which the largest number of processes can be executed before the safety algorithm returns failure.

a$.[2]$ Updated $\backslash (\backslash$mathrm$\{$P$\}\_\{0\}\backslash )$ Allocation:

b$.[2]$ Updated $\backslash ($ P$\_\{0\}\backslash )$ Need:

c$.[2]$ Updated Available:

d$.[4]$ Can the request be granted immediately $(1)$ and why$(3)?$