Consider the multiplication operator $L_A:\mathbb{C}^2\to\mathbb{C}^2$ where $$A=\left[\begin{array}{cc} 7 &-2\cr 10 &-1 \end{array}\right].$$ Find a basis $B$ for a one dimensional $L_A$-invariant subspace.
$B = \lbrace$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\}$