A water resources engineer is considering a new runoff diversion plan as shown schematically in the figure below. The plan requires runoff to flow through five different materials which are capable of absorbing different amounts of the incoming flow $($Q$).$ The key design consideration is to determine what the remaining runoff $(Q2)$ will be for different input flow $(Q1)$ amounts. Solve the problem by first defining a set of linear equations using conservation of mass at each of the different runoff materials. Use these sets of linear equations to define a matrix that describes the system and use NumPy to solve the set of linear equations to determine the intermediate flow values $($QA to QG$)$ and the output flow Q$2$ given Q$1$ is $10\frac{m^3}{s}.$ Report your answers in a table $[$Course Objective #$3$ and #$5]$:

$*$in jupyter lab please!!$*$