g(\alpha \left( \begin{array}{cc}a_1 & a_2 \\ a_3 & a_4 \end{array} \right)+ \beta \left( \begin{array}{cc}b_1 & b_2 \\ b_3 & b_4 \end{array} \right) ) = g( \left( \begin{array}{cc}\alpha a_1+ \beta b_1 & \alpha a_2+ \beta b_2 \\\alpha a_3+ \beta b_3 & \alpha a_4+ \beta b_4 \end{array} \right)) = \left( \begin{array}{cc}\alpha a_1+ \beta b_1 & \alpha a_2+ \beta b_2 \\\ 0 & \alpha a_4+ \beta b_4 \end{array} \right) =