\ker \left( {A - 2I} \right) = \left\{ {\left[ {\begin{array}{*{20}c}
 {x_1 } \\
 {x_2 } \\
 {x_3 } \\

 \end{array} } \right]:\left[ {\begin{array}{*{20}c}
 { - 1} & 2 & 3 \\
 0 & { - 1} & 2 \\
 0 & 0 & 0 \\

 \end{array} } \right]\left[ {\begin{array}{*{20}c}
 {x_1 } \\
 {x_2 } \\
 {x_3 } \\

 \end{array} } \right] = \left[ {\begin{array}{*{20}c}
 0 \\
 0 \\
 0 \\

 \end{array} } \right]} \right\} =