\left( \begin{array}{cc} a_1 & a_2 \\\ 0 & a_4 \end{array} \right) = a_1 \left( \begin{array}{cc} 1 & 0 \\\ 0 & 0 \end{array} \right) + a_2 \left( \begin{array}{cc} 0 & 1 \\\ 0 & 0 \end{array} \right) + a_4 \left( \begin{array}{cc} 0 & 0 \\\ 0 & 1 \end{array} \right)