Problem 5 Solve the following set of algebraic equations X1 + X2 + 5X3-X4-11 2x1 -...
USING MATLAB/SCILAB: Given the following set of linear equations, solve using LU DECOMPOSITION x1 + 2x2 - x3 + x4 = 5 -x1 - 2x2 - 3x3 + 2x4 = 7 2x1 + x2 - x3 - 5x4 = -1 x1 + x2 + x3 + x4 = 10 Please show me pictures of the matlab/scilab compiler or copy-paste code and output
Q1. (25 points) Solve the given set of linear algebraic equations X1 + 2x2 + 3x3 = 0 4x1 + 5x2 + 6x3 = 0 7x: + 8x2 + 9x3 = 0 by expressing it in the form Ax = 0 and reducing A to its row-reduced echelon form through suitable elementary row operations. Show all your work.
Use an algorithm that you would systematically follow to apply the technique and solve each set of systems of linear equations. For example, you may select the technique of finding the inverse of the coefficient matrix A, and then applying Theorem 1.6.2: x = A^-1 b. There are several ways that we have learned to find A^-1. Pick one of those ways to code or write as an algorithm. Or another example, you may select Cramer’s rule. Within Cramer’s rule,...
Please do all steps 3. Use Gauss Elimination method to solve X1 + 1.5%-3x,--10 2X1-X2-2X3 = 5 2x1 - 2x2 + 5x3 6 i, Put the equation in the matrix form ii. Show the forward elimination steps i. Show the backward substitution steps
Write the system of linear equations in the form Ax = b and solve this matrix equation for x. x1 – 2x2 + 3x3 = 24 -X1 + 3x2 - x3 = -11 2x1 – 5x2 + 5x3 = 42 X1 x2 = X3 ] 24 -11 42 [ x
Solve using Gauss Jordan 3) Given the following set of linear equations x, +2x2-x3 +x4=5 -xi-2x2-3x3 + 2x4 = 7 x, +x2 + x3+x4=10
Solve the system X1 + 2x2 – 3x3 = 5 2x1 + x2 – 3x3 = 13 - X1 + x2 = -8 [1 X=t1 tec 1 a. b. SEC Oc. 1 - -- 1. Jeee -2 -0. x=t0 O d. -1 , SEC e. SEC o f. X=S 2 3 ], sec -5
Problem 5: a) (2 Points) Using the two-phase simplex procedure solve Minimize 3X1 + X2 + 3X3-X4 Subject to 1 2.x2 - ^3 r4 0 2x1-2x2 + 3x3 + 3x4 9 T1, x2, x3, x4 2 0. b) (2 Points) Using the two-phase simplex procedure solve Minimize Subject to x1+6x2-7x3+x4+5x5 5x1-4x2 + 132:3-2X4 + X5-20 X5 〉 0.
Consider the mathematical program max 3x1 x2 +3x3 s.t. 2X1 + X2 + X3 +X4-2 x1 + 2x2 + 3x3 + 2xs 5 2x1 + 2x2 + x3 + 3x6 = 6 Three feasible solutions ((a) through (c)) are listed below. (b) xo) (0.9, 0, 0, 0.2,2.05, 1.4) (c) xo) (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution.
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks) Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)