Using Mason's Gain Formula, determine the transfer function from input $R(s)$ to output $Y(s)$ given the following signal flow graph. Determine the loop gains, $\mathrm{D}$, the forward path gains $\mathrm{Mi}$, and the corresponding Di. In terms of your solution please express the solution in terms of the of forward-path and loop gains (e.g. M1 and L11, etc...). For instance you would define LX1 = -G2G3G4G5H2, keep your final answer more compact by referring to $L \times 1$. Determine the numerical value of the transfer function of all gains $\mathrm{G} 1$ to $\mathrm{G} 8$ are each equal to 2 (i.e. $\mathrm{G} 2=2$ ) and that all feedback gains $\mathrm{H} 1$ through $\mathrm{H} 4$ are equal to unity $(\mathrm{H} 1=1)$. Hint....there are 8 loops and 3 pairs of two non-touching loops.

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