Develop, debug, and test a program in either a high-level language or macro language of your choice to solve a system of equations with Gauss elimination with partial pivoting. Base the program on the pseudocode from Fig. 9.6. Test the program using the following system (which has an answer of
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- For the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3: Q1) Using Matlab to employ the Euler Method (Sect 2.4) Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5 close all clear all % Let's program exact soln for i=1:5 x_exact(i)=0.5*i-0.5; y_exact(i)=-x_exact(i)-1+exp(x_exact(i)); end plot(x_exact,y_exact,'b') % now for Euler's h=0.5 x_EM(1)=0; y_EM(1)=0; for i=2:5 x_EM(i)=x_EM(i-1)+h; y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1))); end hold on plot (x_EM,y_EM,'r') % Improved Euler's Method h=0.5 x_IE(1)=0; y_IE(1)=0; for i=2:1:5 kA=x_IE(i-1)+y_IE(i-1); u=y_IE(i-1)+h*kA; x_IE(i)=x_IE(i-1)+h; kB=x_IE(i)+u; k=(kA+kB)/2; y_IE(i)=y_IE(i-1)+h*k; end hold on plot(x_IE,y_IE,'k')arrow_forwardQ3) Find the optimal solution by using graphical method:. Max Z = x1 + 2x2 Subject to : 2x1 + x2 < 100 X1 +x2 < 80 X1 < 40 X1, X2 2 0arrow_forwardHelp me solve this USING MATLABarrow_forward
- Please answer with The Network Simplex Methodarrow_forwardDISCUSSION Before posting to the discussion board, complete the following: The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0arrow_forward1) Model the following problem with integer programming. The marketing department has been allocated a budget of $10M and would like to determine which products to develop advertising campaigns; note: at most one campaign can be launched for each product. Their goal is to maximize revenue for the company. Data is presented in the table below. Product A BCD E F 10 7 12 8 6 Projected Revenue ($M) Cost ($M) 6 1 2 5 4 3arrow_forwardProblem1: Solve the system of linear equations by each of the methods listed below. (a) Gaussian elimination with back-substitution (b) Gauss-Jordan elimination (c) Cramer's Rule 3x, + 3x, + 5x, = 1 3x, + 5x, + 9x3 = 2 5x, + 9x, + 17x, = 4arrow_forwardIntroduce slack variables as necessary and then write the initial simplex tableau for the given linear Maximize z = x₁ + 9x2 programming problem. subject to x₁ + 2x₂ ≤ 12 6x₁ + x₂ ≤ 10 2x₁ + 2x₂ ≤8 with x₁ ≥0, X₂ ≥0 Complete the initial simplex tableau. X₁ X2 S₁ $2 $3 1 2 1 6 0 1 10 0 0 8 0 0 0 1 0 N NAT 2 ܘ ܘ ܤ N оооarrow_forwardQ-Find the solution by using the simplex method? 1- Max Z=3X1+2X2 S. T: X1+X2 ≤ 4 X1-X2 ≤2 X1, X2 ≥0 2- MAX Z= 2X1+3X2+X3 S. T: 3X1+6X2+X3 ≤ 6 4X1+2X2+X3 ≤ 4 X1-X2+X3 ≤ 3 X1, X2,X3 20arrow_forwardPlease solve the following two problems:arrow_forwardDetermine if the system is consistent or inconsistent. Justify your answer and find all solutions to the system of linear equations. Justification should be written on your solution paper. Transform the matrix into ROW ECHELON FORM (REF) using row operations. 2x +8y+ 6z = 20 4x+2y-2z =-2 3x-y+z = 11 Enter final answer: (x, y, z) =(arrow_forward1.Please solve the following:arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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