Chapter 8, Problem 3RE

Consider the linear system $X^{\prime }=\left(\begin{array}{ccc}4& 6& 6\\ 1& 3& 2\\ -1& -4& -3\end{array}\right)X$. Without attempting to solve the system, determine which one of the vectors

$\begin{array}{l}{K}_1=\left(\begin{array}{c}0\\ 1\\ 1\end{array}\right),K_2=\left(\begin{array}{c}1\\ 1\\ -1\end{array}\right),K_3=\left(\begin{array}{c}3\\ 1\\ -1\end{array}\right),K_4=\left(\begin{array}{c}6\\ 2\\ -5\end{array}\right)\\ \end{array}$

is an eigenvector of the coefficient matrix. What is the solution of the system corresponding to this eigenvector?