Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 2.4, Problem 6P
Explanation of Solution
Determining the dependency of the given sets of
Consider the given sets of vectors,
A matrix A is formed as given below; whose rows are the above given vectors:
The Gauss-Jordan method is applied to find the dependency of the above given sets of vectors.
Replace row 2 by (
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
6. (Linear independence ): Is it true that if x; y; and z are linearly independent vectors overGF(q), then so are x + y; y + z, and z + x ?
Determine the value(s) of x so that the matrix below is the augmented matrixof an inconsistent linear system.
x
1
5
5
-3
2
Bu = ƒ and Cu = f might be solvable even though B and C are singular. Show that every vector f = Bu has ƒ1 + ƒ2+ ……. +fn = 0. Physical meaning: the external forces balance. Linear algebra meaning: Bu = ƒ is solvable when ƒ is perpendicular to the all – ones column vector e = (1, 1, 1, 1…) = ones (n, 1).
Chapter 2 Solutions
Operations Research : Applications and Algorithms
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.2 - Prob. 1PCh. 2.3 - Prob. 1PCh. 2.3 - Prob. 2P
Ch. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Prob. 9PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2 - Prob. 1RPCh. 2 - Prob. 2RPCh. 2 - Prob. 3RPCh. 2 - Prob. 4RPCh. 2 - Prob. 5RPCh. 2 - Prob. 6RPCh. 2 - Prob. 7RPCh. 2 - Prob. 8RPCh. 2 - Prob. 9RPCh. 2 - Prob. 10RPCh. 2 - Prob. 11RPCh. 2 - Prob. 12RPCh. 2 - Prob. 13RPCh. 2 - Prob. 14RPCh. 2 - Prob. 15RPCh. 2 - Prob. 16RPCh. 2 - Prob. 17RPCh. 2 - Prob. 18RPCh. 2 - Prob. 19RPCh. 2 - Prob. 20RPCh. 2 - Prob. 21RPCh. 2 - Prob. 22RP
Knowledge Booster
Similar questions
- Given vectors :u = (5,2) ; v = (-2,5) w = (0,3) ; q = (10,4)4.1 Calculate the following dot products:u.v ; (u.v).w ; u.(3w) , u.(w-v)4.2 Calculate‖?‖ ; d(u,v) ; ‖? − ?‖24.3 u and v are they orthogonal4.4 u and w are they orthogonal4.5 find c real number that satisfy q = c.u4.6 Deduce that q and u are parallel4.7 Normalize vector warrow_forwardUsing the algorithm for Gauss-Jordan without pivoting, code a function myGaussJordanNoPivotthat takes as input a matrix A and collection of q right-hand sides bl forming the q columns of of a matrix B. Yourfunction shall return the q solution vectors xl as columns of a matrix X. Do not use any Matlab build-in functionsfor solving matricesarrow_forwardUSING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.arrow_forward
- Solve in C++ using the given code and avoid using vectorsarrow_forwardIf there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A, n x n square matrix is diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues of the matrix A. A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) : 1 -1 -1 1 3 1 -3 1 -1 a)Write a program that calculates the eigenvalues and eigenvectors of matrix A using NumPy. b)Write the program that determines whether the D matrix is diagonal by calculating the D matrix, using NumPy. #UsePythonarrow_forwardPlease Help me With This Problem Write a function to find the norm of a matrix. The norm is defined as the square root of the sum of squaresof all elements in the matrixarrow_forward
- Minimize the following function using the Karnaugh Map. Show complete solution pleasearrow_forwardGenerate H (Hilbert Matrix) for n = 15.Compute the right-hand size vector b = Hx so that the exact solution is xˆ = 1 (thevector of ones). Solve the linear system in MATLAB as a least squares problem usingSVD and report the relative error in the approximate solution in the Euclidean norm.Compare your result to the solution obtained by H\b.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole