$8.$ Given the following state for the Banker's Algorithm:

$4$ processes P$0$ through P$3$

$3$ resource types: A $(9$ instances$)$; B$(2$ instances$)$; C $(5$ instances$)$

Snapshot at time TO:

Available

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline A & B & C $\backslash \backslash$

$\backslash$hline $2$ & $1$ & $1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$ Current allocation $\}$ & $\backslash$multicolumn$\{3\}\{$c$|\}\{$ Maximum Demand $\}\backslash \backslash$

$\backslash$hline Process & A & B & C & A & B & C $\backslash \backslash$

$\backslash$hline P$0$ & $1$ & $0$ & $1$ & $2$ & $1$ & $1\backslash \backslash$

$\backslash$hline P$1$ & $2$ & $1$ & $2$ & $5$ & $2$ & $4\backslash \backslash$

$\backslash$hline P$2$ & $3$ & $0$ & $0$ & $3$ & $1$ & $1\backslash \backslash$

$\backslash$hline P$3$ & $1$ & $0$ & $1$ & $1$ & $1$ & $1\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$-$ Create the need matrix $($max$-$allocation$)$

$-$ Determine if the current state is safe by providing a safe sequence of execution, if there is no safe sequence explain.

$-$ If the current state is safe can the following requests be granted, why or why not? $($consider the requests separately$)$

a$.$ P$1$ requests $\backslash ((1,0,1)\backslash )$

b$.$ P$1$ requests $\backslash ((0,1,1)\backslash )$