2x1 − x2 − 3x3 − 2x4 = 1
x1 − x2 − 4x3 − 2x4 = 5
3x1 − x2 − x3 − 3x4 = −2
x1 + 2x3 − x4 = −4
numerical methods 1) Aşağıdaki denklem sisteminin köklerini Gauss-Eliminasyon yöntemi ile bulunuz. x1 + 2x2 + 3x3 + 4x4 + 5xs = 7 2x1 + xy + 2x3 + 3x4 + 4xs = -1 3x1 + 2x2 + x3 + 2x4 + 3x3 = -3 I 4x1 + 3x2 + 2x3 + x4 + 2x5 = 5 5x1 + 4x2 + 3x3 + 2x4 + xs = 17
Use the Gaussian elimination method to solve each of the following systems of linear equations. In each case, indicate whether the system is consistent or inconsistent. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. 1-5x1 – 2x2 + 2x3 = 14 *(a) 3x1 + x2 – x3 = -8 2x1 + 2x2 – x3 = -3 3x1 – 3x2 – 2x3 = (b) -6x1 + 4x2 + 3x3 = -38 1-2x1 +...
(a) State the dual problem. (b) Solve both the primal and the dual problem with any method that works. (c) Check that your optimal solutions are correct by verifying they are feasible and the primal and dual objective functions give the same value. 9. Minimize z subject to 4x1 + x2 + x3 + 3x4 2x, + x2 + 3x3 + x4 2 12 3xi + 2x2 + 4x3 2x1-x2 + 2x3 + 3x4-8 3x1 + 4x2 + 3x3 х,2...
Find the solutions of 2x1-3x2-7x3+5x4+2x5=-2 x1-2x2-4x5+3x4+x5=-2 2x1+0x2-4x3+2x4+x3=3 x1-5x2-7x3+6x4+2x5=-7
Consider the following linear transformation T: RS → R3 where T(X1, X2, X3, X4, X5) = (x1-X3+X4, 2X1+X2-X3+2x4, -2X1+3x3-3x4+x5) (a) Determine the standard matrix representation A of T(x).
Solve both A and B using Gauss-Jordan elimination 2x1+ 5x2+ 2x3-5。3x1+2xī4x3-3x4-82 2x1- X2+2x3+2x4 11
[-/1 Points] DETAILS ROLFFM8 2.2.052. Solve the following system of equations by reducing the augmented matrix. X1 + 3x2 - x3 + 2x4 -3 - 3x1 + X2 + x3 + 3x4 = -2 2x3 + X4 = - 4x4 = -6 2X1 4x2 2X2 1 (X1, X2, X3, X4) = D) Need Help? Talk to a Tutor
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.
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.
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25 Problem 1 (20 pts) Consider...