Use duality to solve problem 4 4. Minimize z-8x1 + 4x2 + 16x3 subject to 2x1 + 2x2 + 3x3 216 3x1 +x2 t 4xs 2 14 3x +x2 + 5x3 2 12 xi,x2, x320 Use duality to solve problem 4 4. Minimize z-8x1 + 4x2 + 16x3 subject to 2x1 + 2x2 + 3x3 216 3x1 +x2 t 4xs 2 14 3x +x2 + 5x3 2 12 xi,x2, x320
Write the system of equations as a matrix equation of the form AX = B. X1 - 2x2 + 3x3 = - 4 - 2X1 + 4x2 = 1 X1 + X2 + 3x3 = - 3 X1 X2 = X3 (Type an integer or decimal for each matrix element.)
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 +...
Your last submission is used for your score. 1. + -/1 points ZillEngMath6 8.2.003. Use either Gaussian elimination or Gauss-Jordan elimination to solve the given system or show that no solution exists. (Ift Infinite number of solutions, use t for the parameter.) 9x1 + 3x2 = -4 2x1 + x2 = -1 (X1, X2) = eBook 2. 0/1 points Previous Answers ZillEngMath6 8.2.005. Use either Gaussian elimination or Gauss-Jordan elimination to solve the given system or show that no solution...
dx = 1. (10pts) 3. Given the system of linear equations 5x1 + 2x2 + x3 = 45 -2x, + x2 – 3x3 = -4 (5pts) 4xy – X2 + 8x2 = 2 Write the augmented matrix b. Solve the system by Gaussian elimination & backward substitution method. 21 a. 30
3. Solve the following systems of equations using Gaussian elimination. (a) 2x 3x2 + 2x3 = 0 (d) 2x + 4x2 2.xz 4 *- x2 + x3 = 7 X; - 2x2 · 4x3 = -1 -X, + 5x2 + 4x3 = 4 - 2x - X2 3x3 = -4
Use Gaussian elimination to solve the equations 4.21 + 4.22 - 2x3 = -1 3x1 + 4x2 – 3x3 = 3 -2x1 - 3x2 + x3 = 1
[M2] Let -1] 2 A = 2 1 -2 3 (a) Find A-1, (b) Use the inverse matrix above to solve the system -2x1 + 2x2 – x3 2, X1 + x2 + 2x3 = -1, 2^1 — 2л2 + 3х3 — 5. (c) Write the following matrix A as a product of elementary matrices. |0 A = |1 -2 0 3 5
Q.1 Using the method of Triangular Decomposition solve the set of equations. Xı - 2x2 + 3x3 - X4 = -3 3x1 + x2-3x3 +2x4 = 14 5xi +3x2+2x3 + 3x4 = 21 2x1 - 4x2 – 2x3 + 4x4 = -10 If Ax = 2x, determine the eigenvalues and corresponding eigenvectors of -3 0 6 4 10 - 8 A 4 5 3 B= 1 2 1 1 2 1 -1 2 3 Q.2
(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. 8. Minimize z -8x1 + 6x2 + 11x3 subject to 5x1 x2 + 3x3 s 4 5x1 + x2 + 3x3「2 2x1 + 4x2 + 7x3 s.5 2x1 + 4x2 + 7x3 2 3 x1 + x2...