$dimV<\infty$, $f,g$ are nonzero linear functional on $V$ real vector space, $Ker(f)\subsetneq Ker(g)$ we need to pick out true statements
$Ker(f)=Ker(g)$
$ker(g)/ker(f)\cong\mathbb{R}^k, 1\le k
there exist a constant $c$ such that $g=cf$
In any case Kernel has to be of dimension $n-1$ assuming $dimV=n$, so $1$ and $3$ are true,and hence $2$ is wrong trivially., am I right?