Consider the multiplication operator $L_A:\mathbb{R}^4\to\mathbb{R}^4$ where $$A=\left[\begin{array}{cccc} -2 &1 &-2 &0\cr -4 &-10 &2 &-15\cr 1 &-6 &3 &-6\cr 3 &4 &0 &7 \end{array}\right].$$ Find a matrix $B$ whose row space is smallest $L_A$-invariant subspace that contains the vector $\left(1,1,-1,-1\right)$.
$B =$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$