Start from orthotropic stiffness matrix (36 constants), we reduced to stiffness matrix to 13 constants. Start from orthotropic stiffness matrix, derive(reduce) the stiffness matrix to 9 constants.material. Please show all

operations in details. \left[\begin{array}{c} \sigma_{1} \\ \sigma_{2} \\ \sigma_{3} \\ \tau_{23} \\ \tau_{31} \\ \tau_{12} \end{array}\right]=\left[\begin{array}{llllll} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ C_{12} & C_{2} & C_{23} & 0 & 0 & 0 \\ C_{13} & C_{23} & C_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{41} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{55} & 0 \\ 0 & 0 & 0 & 0 & 0 & C_{66} \end{array}\right]\left[\begin{array}{c} \varepsilon_{1} \\ \varepsilon_{2} \\ z_{33} \\ \gamma_{31} \\ y_{12} \end{array}\right] \left[\begin{array}{c} \sigma_{1} \\ \sigma_{2} \\ \sigma_{3} \\ \tau_{23} \\ \tau_{31} \\ \tau_{12} \end{array}\right]=\left[\begin{array}{llllll} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ C_{12} & C_{2} & C_{23} & 0 & 0 & 0 \\ C_{13} & C_{23} & C_{31} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{41} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{55} & 0 \\ 0 & 0 & 0 & 0 & 0 & C_{66} \end{array}\right]\left[\begin{array}{c} \varepsilon_{1} \\ \varepsilon_{2} \\ z_{33} \\ \gamma_{31} \\ y_{12} \end{array}\right]