Homework Answers
To show i., ii., iii., here e reduced the augmented matrix of
the system by Gauss elimination method. The calculation is very
taff. But I solve it correctly. Hope you understand. Thank
you.
Determine a, b E R so that the system 6x1 + (2a - 3)x2 + 4ax3...
Determine a, b E R so that the system 6x1 + (2a - 3)x2 + 4ax3 + 324 = 2 + b 4x1 + (2a - 2)x2 + 2axy + 2x4 = 2 4x1 - 2x2 + (4a + 2)x3 + (2a + 2)x1 = 0 201 - 22 + (2a +3)x3 + 2ax 1 = -2b - 2 has (i) a unique solution, (ii) infinitely many solutions, (iii) no solution
Use the Gaussian elimination method to solve each of the following systems of linear equations. In...
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 w...
(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...
[-/1 Points] DETAILS ROLFFM8 2.2.052. Solve the following system of equations by reducing the augmented matrix....
[-/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
Find the duals of the following LP. (a) Max Z--2x1 + x2 - 4xz + 3x4...
Find the duals of the following LP.
(a) Max Z--2x1 + x2 - 4xz + 3x4 st. x1 + x2 + 3x2 + 2x4 S4 X1 -X3 + X, 2-1 2x1 + x2 32 X1 + 2x2 + x3 + 2x4 = 2 X2, X3, X, 20 (b) Min Z=0.4x1 +0.5x2 st. 0.3x2 +0.1x, 32.7 0.5x7 +0.5x2 = 6 0.6x, +0.4x, 26 X1, X220
1. (10+10pts.) Consider the homogeneous system x1 + x2 + (3 – 2a)x3 = 0 2x1...
1. (10+10pts.) Consider the homogeneous system x1 + x2 + (3 – 2a)x3 = 0 2x1 + x2 + 7x3 - 24 = 0 -X2 + 2ax3 + 2x4 = 0 x1 + x2 + 4x3 = 0 where a is a real constant. a. Find the value of a for which the dimension of the solution space of the system is 1. b. Find a basis of the solution space of the system for the value of a found...
Problem 5: a) (2 Points) Using the two-phase simplex procedure solve Minimize 3X1 + X2 +...
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.
Thank you! Solve using Gauss-Jordan elimination 2x1 + 6x2 - 26x3 = 18 4x1 + 3x2...
Thank you! Solve using Gauss-Jordan elimination 2x1 + 6x2 - 26x3 = 18 4x1 + 3x2 - 16x3 = 0 x1 + x2 - 5x3 = 1 Select the correct choice below and fill in the answer A) The unique solution is x1=_________, x2 = ________, and x3 - _________. B) The system has infinitely many solutions. The solution is x1 = __________, x2 = _____________, and x3 = t. (Many thanks for the help) Sandi
Find all solutions to the system using the Gauss-Jordan elimination algorithm. 3x3 + 15x4 =0
Find all solutions to the system using the Gauss-Jordan elimination algorithm. 3x3 + 15x4 =0 x1 + x2 + x3 + x4 =1 4x1 - x2 + x3 + 4x4 = 0 4x1 - x2 + x3 + x4 =0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The system has a unique solution x1=_______ ,x2=_______ ,x3=_______ ,x4=_______ B. The system has an infinite number of solutions characterized as follows.C. The system has an infinite number of...
Determine the values of a for which the following system of linear equations has no solutions,...
Determine the values of a for which the following
system of linear equations has no solutions, a unique solution, or
infinitely many solutions. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values.
x1+ax2−x3
=
2
−x1+4x2−2x3
=
−5
−2x1+3x2+x3
=
−4
No Solutions:
Unique Solution:
Infinitely Many Solutions:
Determine a, b E R so that the system 6x1 + (2a - 3)x2 + 4ax3 + 324 = 2 + b 4x1 + (2a - 2)x2 + 2axy + 2x4 = 2 4x1 - 2x2 + (4a + 2)x3 + (2a + 2)x1 = 0 201 - 22 + (2a +3)x3 + 2ax 1 = -2b - 2 has (i) a unique solution, (ii) infinitely many solutions, (iii) no solution
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...
[-/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
Find the duals of the following LP.
(a) Max Z--2x1 + x2 - 4xz + 3x4 st. x1 + x2 + 3x2 + 2x4 S4 X1 -X3 + X, 2-1 2x1 + x2 32 X1 + 2x2 + x3 + 2x4 = 2 X2, X3, X, 20 (b) Min Z=0.4x1 +0.5x2 st. 0.3x2 +0.1x, 32.7 0.5x7 +0.5x2 = 6 0.6x, +0.4x, 26 X1, X220
1. (10+10pts.) Consider the homogeneous system x1 + x2 + (3 – 2a)x3 = 0 2x1 + x2 + 7x3 - 24 = 0 -X2 + 2ax3 + 2x4 = 0 x1 + x2 + 4x3 = 0 where a is a real constant. a. Find the value of a for which the dimension of the solution space of the system is 1. b. Find a basis of the solution space of the system for the value of a found...
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.
Determine the values of a for which the following
system of linear equations has no solutions, a unique solution, or
infinitely many solutions. You can select 'always', 'never', 'a =
', or 'a ≠', then specify a value or comma-separated list of
values.
x1+ax2−x3
=
2
−x1+4x2−2x3
=
−5
−2x1+3x2+x3
=
−4
No Solutions:
Unique Solution:
Infinitely Many Solutions:
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