(Solved): Find the coordinate vector of A relative to the basis \( S=\left\{A_{1}, A_{2} A_{3}, A_{4}\right\} ...

Find the coordinate vector of A relative to the basis \( S=\left\{A_{1}, A_{2} A_{3}, A_{4}\right\} \). \[ \begin{array}{l} A=\left[\begin{array}{ll} 9 & 0 \\ 5 & 0 \end{array}\right], A_{1}=\left[\begin{array}{ll} 3 & 3 \\ 3 & 3 \end{array}\right], A_{2}=\left[\begin{array}{ll} 0 & 3 \\ 3 & 3 \end{array}\right], A_{3}=\left[\begin{array}{ll} 0 & 0 \\ 1 & 1 \end{array}\right], A_{4}=\left[\begin{array}{ll} 0 & 0 \\ 0 & 5 \end{array}\right] \\ (A)_{5}=1 \end{array} \]