Convert the following nfa to an equivalent dfa $($draw a state diagram for your answer$).$ Show and explain$/$justify your answer and all the steps used to derive the dfa. $=\{$a$,$b$\}.$

$1.$ Mnfa$=(\{$q$0,$q$1,$q$2\},\{$a$,$b$\},\backslash$delta $,$q$0,\{$q$2\})$ with the following transitions:

$($q$0,$a$)=\{$q$0,$q$1\}$

$($q$1,$b$)=\{$q$1\}$

$($q$1,\backslash$lambda $)=\{$q$2\}$

$($q$2,$a$)=\{$q$0,$q$2\}$