Consider the multiplication operator $L_A:\mathbb{R}^4\to\mathbb{R}^4$ where $$A=\left[\begin{array}{cccc} 7 &8 &-1 &17\cr 4 &15 &-4 &26\cr -5 &6 &-4 &5\cr -5 &-8 &1 &-16 \end{array}\right].$$ Let $W$ be the subspace of $V=\mathbb{R}^4$ generated by $\lbrace \left(1,1,-1,-1\right),\left(1,-1,-2,0\right) \}$. It is easy to see that $W$ is invariant under $L_A$. Define the linear operator $K$ on the quotient space $V/W$ by $K(u+W):= L_A(u)+W$. Find the characteristic polynomial $f(t)$ of $K$.
$f(t) =$