Concept explainers
Explanation of Solution
Using Gauss-Jordan method to indicate the solutions:
Consider the given system of linear equations,
The augmented matrix of this system is as follows:
The Gauss-Jordan method is applied to find the solutions of the above system of linear equations.
Replace row 3 of A|b by (row 3 – row 1), then the following matrix is obtained,
Now, replace row 3 of
This produces the following result,
Solving the above equations, the following result is obtained,
Therefore, the above system of linear equations has a unique solution.
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Chapter 2 Solutions
Operations Research : Applications and Algorithms
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- Show that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z havethe value 1.arrow_forwardGiven A = {1,2,3} and B={u,v}, determine. a. A X B b. B X Barrow_forwarda) Solve the following system using naive Gaussian elimination with three digits (rounded )arithmetic and compare the result with the exact solution x1 = 1.00010... and x2 = 0.99989... 10^(-4 *)x1 + x2 = 1 x1 + x2 = 2 b) repeat a)after interchanging the order of two equationsarrow_forward
- Two points on line 1 are given as (x1, y1) and (x2,y2) and on line 2 as (x3, y3) and (x4, y4), as shown in Figure 3.8a and b.The intersecting point of the two lines can be found by solving the following linearequations:(y1 - y2)x - (x1 - x2)y = (y1 - y2)x1 - (x1 - x2)y1(y3 - y4)x - (x3 - x4)y = (y3 - y4)x3 - (x3 - x4)y3This linear equation can be solved using Cramer’s rule . If the equation has no solutions, the two lines are parallel (see Figure). Write a program that prompts the user to enter four points and displays the intersectingpoint. Here are sample runs:arrow_forwardWhich option is correct for the following system equation? x-y-z=4 2x-2y-2z=8 5x - 5y - 5z = 20 answer a)Finite solutions b)No solution c)Subzero solutions d)Infinitely many solutions e)Unique solutionarrow_forwardx2+9x-8 0.2x3+2x2+2x+10 solve this two linear equation using the initial point x = 3arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole