The following picture represents a network of interconnected pipelines. The arrows represent the flowmeasured by ft³ per minutes. The values above the arrows represent the flow in the given segment,the flow is regulated by the valves at the intersections.Of course the amount of water per minute entering each connection, has to be equal to the amount ofwater exiting the connection. This leads to five equations.1020406Write down the system of linear equations that represents the flow at each relevant valve.7Find the augmented matrix and its row reduced echelon form.8How many solutions are there? Notice that the valves allow only one direction for the flow.This means that we require each r; not to be negative. A solution with all positive r; is calledfeasible.9Express all the feasible solutions in terms of inequalities.Suppose you will need to repair the pipe between connections A and B, you will want to have10 the flow between A and B as minimal as possible. What is the minimal value of æg to have afeasible solution.11 Using what you found in the previous answer write all the values of ri, for i = 1, ..., 6 and makesure they are a solution of your system.What happens if you reverse the flow in the segment BD (by substituting the valve)? Find the12 minimal value of r6 that gives you a feasible solution. You probably have seen the formula E- i = }n² + }n This means that if you want to know the sumof the first 100 natural number, this number is1+-1001+2+3+ ...+ 100 =It is told that this formula was proven by Gauss at the age of 5, when the kindergarten teacher gaveher students this problem, tired of the noise that they were making. Turns out, there are infinitelymany of these formulas. If you want to know the value of the sum of the first n numbers raised to thek-th power¿* = ao + a¡n + . .+ ak+1nk+1ikFor example:11E² = 1+22 + 32 + · . + n² =+교 + 공i=1Notice that when you want to sum the squares of numbers, the formula will yield a polynomial ofdegree 3 and more in general if you sum the kth power of numbers you will get a polynomial of degreek+1.The goal is to find the formula for k = 6.1. Specialize the formula in (*) for k = 6.2. What are the variable you want to solve for?3. How many equations do you need?4. Find a system of 8 different equations.5. Solve the system with Matlab and give the formula.

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Accepted Answer

Picture of network of interconnected pipeline is

Solution 6:
Since we know that at any valve,…