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Use matlab to solve the problem only. No python. Please give out your code, explanations will be better.

PROBLEM 1 Consider the bridge truss diagrammed below: 2 F2 3 F3 Fi Fu F4 F9 F10 F12 F13 NA F. 8 F 7 F6 6 F. Given a vector of external forces (what we call the "data" or the right hand side") b on the bridge, we can compute the forces F1, F2, ..., F13 (the forces on each girder) by solving the system Ax = b, where x = (F1, F2, ... F13) is the column vector of unknown forces and A is the 13 x 13 matrix, which will be called in for you in the solution template. We will solve for the unknown forces assuming that there are three vehicles at positions 13, 11 and 9 with weights 7 tons, e tons and 3 tons, respectively. This means that there is a weight of tons pulling down on girder 13, a weight of e- tons pulling down on girder 11 and a weight of 3 tons pulling down on girder 9, so we need to use b = (0,0,0,0,0,0,0,0,3,0,2,0,7) (remember this is a column vector; be very careful about the shapes). (1) Solve for x and save your answer as a 13 x 1 column vector named A1. (2) Compute the PA= LU factorization of A. Save a copy of the resulting matrix L in a variable named A2. (3) From the PA = LU factorization above, find the vector c in the Ux = c problem (don't forget to permute for MATLAB and Python this will work differently). Save the intermediate vector c in a variable named A3. (4) Now suppose that we add weight to the truck in position 8 (which corresponds to the 9th entry of b) in increments of 0.001 tons until the bridge collapses. Each girder can withstand 20 tons of compression or tension (i.e., positive or negative forces) before breaking. This means that the bridge will collapse when the largest (in absolute value; i.e. max) force in x is larger than 20. Find the smallest weight of the truck at position 8 for which the bridge collapses and save this weight in a variable named A4. Find the index of the girder that breaks first and save it in a variable named A5. (Note: In the problem description we started our indices at 1, but python starts counting indices at 0. You will therefore need to add 1 to the index from python.) Hint: The function max in MATLAB and np. argmax in python will be useful. Also, we are only changing the right hand side, and we already found the PA = LU factorization, so can we use the PA= LU factorization instead of redoing the Gaussian Elimination