Deterministic selection algorithm guarantees its runtime to be O$($n$)$ for every input array of

length n$.$ Given the assumption that there exists a positive constant k that satisfies:

i$)$ T$(1)<=$ k

ii$)$ T$($n$)<=$ kn $+$ T

$9$n

$13$

$+$ T

$3$n

$26$

Then prove that T$($n$)=$ O$($n$).($Please clearly show your steps in detail$)(5$ points$)$