Solving Systems of Equations using Gauss Elimination: solving truss equilibrium equations - project problem 3.3 in Rao. Write a Mathcad routine that can solve the following resulting system of equations of the form: [A]{x} = {b} using Basic Gaussian Elimination (You do NOT need to include Row or Column Pivoting). The [A] matrix and right hand side vector, {b}, are given below for you to use. This is a system of N= 10 equations and N= 10 unknowns, therefore, your final solution vector, {x} should have 10 values. 4 | 이 | | 000 | 1 | 1| 22 2] 이 | -12 | 이 | 이 | 이 | -5| 8 | 8.66 | | 이 10] 이 2 | 3 1 | | -12] 30 | 0이 | 0 34 | 이 이 이 -12 이 이 8.66 | -5 -15 | -8.66 | 이 -5 | 이 8.66 | 30 | 이 -8.66 | -15] 8.66 | -15 | 5 | 6 | 7 | 이 이 -5| | | 8.66 | -12 이 -5 | 이 이 -8.66 | 22 이 이 0이 30 | 0이 이 34 이 이 이 -5 | -8.66 | -12 -8.66 | -15 | 0이 8 | 8.66 | -15] | -8.66 | -15 | 이 | | 30 | 0 | 이 9 | 10 | 이 이 | 0 -5| 8.66 | 8.66 | -15 -5 | -8.66 | -8.66 | -15 | -12] 이 이 이 34 | 이 이 30 | 1 | 11 0 -0.6429 3 | 4 | -0.6429 b = | -0.6429 8 | -0.6429 [10 -0.6429 Required: Verify your code by developing a systems of equations (3 x 3 or 4 x 4 ) with known solutions. You can use Mathcad's intrinsic functions to develop these test cases or make them up using the ideas presented to you in class. That is, make up a matrix Athat is diagonally dominant, make up a solution vector x, multiply the two to find the RHS vector b. Now you have a problem whose solution you know. Once you have the cases, run your Gauss code and verify that it produces the correct results. Gauss Elimination Code to solve [A]{x}={b} without partial pivoting: GAUSS(A, b) := n rows(b) for ke l..n-1 for iek+1..n -Ai, k determine the size of the given problem go across the columns k=1,2...n-1 and for every column "k" use akk as pivot element and row k to eliminate every element in the rows i =k+1, k+2...n below in that column for je 1..n A:,;+ A:,j + s-Ak, j | b; + b; + sub Matrix is now triangulated and upper triangular Back-substitute to solve for ien - 1..1 sum. -- 0 for jen.. i+ 1 sum, + sum, + A1, j'%; b; - sum, return the solution vector triangulated matrix [A] and modified RHS vector {b}