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\left[\begin{array}{c}X_{1} \\ X_{2} \\ \vdots \\ X_{G}\end{array}\right]=\left[\begin{array}{cccc}A_{11} & A_{12} & \cdots & A_{1 G} \\ A_{21} & A_{22} & \cdots & A_{2 G} \\ \vdots & \vdots & \ddots & \vdots \\ A_{G 1} & A_{G 2} & \cdots & A_{G G}\end{array}\right]\left[\begin{array}{c}X_{1} \\ X_{2} \\ \vdots \\ X_{G}\end{array}\right]+\left[\begin{array}{c}F_{11}+F_{12}+\cdots+F_{1 G} \\ F_{21}+F_{22}+\cdots+F_{2 G} \\ \cdots \cdots \\ F_{G 1}+F_{G 2}+\cdots+F_{G G}\end{array}\right]