(Solved): 3. Consider the network of irrigation canals shown below. Assuming the inflow and outflow rates of ...

3. Consider the network of irrigation canals shown below. Assuming the inflow and outflow rates of water are as indicated, and that the direction of flow is as shown, answer the following questions. (a) Write down the system of linear equations that describes the flow rates at each junction/node (i.e. A, B, etc.), and build the corresponding augmented matrix. (b) Use elementary operations to obtain the RREF of the augmented matrix, and write the general solution of the system in terms of parameters $$s=x_3$$ and $$t=x_5$$. (c) Under the assumption that water may only flow in the direction shown, what are the possible values of the parameters?