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\left[\begin{array}{c}X_{1} \\ X_{2} \\ \vdots \\ X_{G}\end{array}\right]=\left[\begin{array}{cccc}I-A_{11} & -A_{12} & \cdots & -A_{1 G} \\ -A_{21} & I-A_{22} & \cdots & -A_{2 G} \\ \vdots & \vdots & \ddots & \vdots \\ -A_{G 1} & -A_{G 2} & \cdots & I-A_{G G}\end{array}\right]^{-1}\left[\begin{array}{c}\sum_{j=1}^{G} F_{1 j} \\ \sum_{j=1}^{G} F_{2 j} \\ \vdots \\ \sum_{j=1}^{G} F_{G j}\end{array}\right]=\left[\begin{array}{cccc}B_{11} & B_{12} & \cdots & B_{1 G} \\ B_{21} & B_{22} & \cdots & B_{2 G} \\ \vdots & \vdots & \ddots & \vdots \\ B_{G 1} & B_{G 2} & \cdots & B_{G G}\end{array}\right]\left[\begin{array}{c}F_{1} \\ F_{2} \\ \vdots \\ F_{G}\end{array}\right]