Solve the following system of
equations using LU factorization without partial
pivoting:
2x1 - 6x2 - x3 =
-38
-3x1 - x2 + x3 =
-34
-8x1 + x2 - 2x3 =
-20
Need a MATLAB code for LU factorization(both partial and
complete pivoting) of 10 random matrices of order 5x5.
Please do not comment like I don't have computer or I don't know
matlab. If you please answer otherwise you can skip.
4-Consider the following problem:
max − 3x1 + 2x2 − x3 + x4
s.t.
2x1 − 3x2 − x3 + x4 ≤ 0
− x1 + 2x2 + 2x3 − 3x4 ≤ 1
− x1 + x2 − 4x3 + x4 ≤ 8
x1, x2, x3, x4 ≥ 0
Use the Simplex method to verify that the optimal objective
value is unbounded. Make use of the final tableau to construct an
unbounded direction..
Consider the linear system of equations below
3x1 − x2 + x3 = 1
3x1 + 6x2 + 2x3 = 0
3x1 + 3x2 + 7x3 = 4
i. Use the Gauss-Jacobi iterative technique with x
(0) = 0 to find
approximate solution to the system above up to the third step
ii. Use the Gauss-Seidel iterative technique with x
(0) = 0 to find
approximate solution to the third step
Consider the linear system of equations
2x1 − 6x2 − x3 = −38
−3x1 − x2 + 7x3 = −34
−8x1 + x2 − 2x3 = −20
With an initial guess x (0) = [0, 0, 0]T solve the system using
Gauss-Seidel method.
1. Solve the following system:
2x1- 6x2- x3 = -38
-3x1–x2 +7x3 = -34
-8x1 +x2 – 2x3 = -20
By:
a. LU Factorization
b. Gauss-Siedel Method, error less that10-4
Hint (pivoting is needed, switch rows).