HeroofTime55

$\mathbf {X} (t)={\begin{bmatrix}X_{1}(t)\\X_{2}(t)\\X_{3}(t)\\\end{bmatrix}}$

$\mathbf {L} ={\begin{bmatrix}F_{1}&F_{2}&F_{3}\\P_{1}&0&0\\0&P_{2}&0\\\end{bmatrix}}$

$\mathbf {X} (1)=\mathbf {L} \times \mathbf {X} (0)$

$\mathbf {X} (2)=\mathbf {L} \times \mathbf {X} (1)=\mathbf {L} \times \mathbf {L} \times \mathbf {X} (0)=\mathbf {L} ^{2}\times \mathbf {X} (0)$

$\mathbf {X} (n)=\mathbf {L} ^{n}\times \mathbf {X} (0)$