Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
4th Edition
ISBN: 9780534423551
Author: Wayne L. Winston
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 2.6, Problem 3P
Explanation of Solution
Proof:
Consider a
The third-row cofactors are as follows:
Therefore, we get
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.)
Sufficient Condition for Diagonalization
If an n xn matrix A has n distinct eigenvalues, then the corresponding eigenvectors are linearly independent and A is diagonalizable.
Find the eigenvalues. (Enter your answers as a comma-separated list.)
Is there a sufficient number to guarantee that the matrix is diagonalizable?
O Yes
O No
Need Help? Read it
Find the value of 'a', if B
is a singular matrix?
%3D
(A) 5
9 (a)
(C) 7
Find the product of the product of the elements of a matrix and the other elements of a matrix with random integer elements of 4 x 2 each
Chapter 2 Solutions
Student Suite Cd-rom For Winston's 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
- . The determinant of an n X n matrix can be used in solving systems of linear equations, as well as for other purposes. The determinant of A can be defined in terms of minors and cofactors. The minor of element aj is the determinant of the (n – 1) X (n – 1) matrix obtained from A by crossing out the elements in row i and column j; denote this minor by Mj. The cofactor of element aj, denoted by Cj. is defined by Cy = (-1y**Mg The determinant of A is computed by multiplying all the elements in some fixed row of A by their respective cofactors and summing the results. For example, if the first row is used, then the determi- nant of A is given by Σ (α(CI) k=1 Write a program that, when given n and the entries in an n Xn array A as input, computes the deter- minant of A. Use a recursive algorithm.arrow_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_forwardQ1: A) Find Eigen values and Eigen vector of the matrix. A = [3 4arrow_forward
- Find the product of the elements of a matrix by other elements of a matrix with integer random elements and the size of each (4 x 2) of them.arrow_forwardFind the matrix product of integer random elements and the size of each (4 x 2) of them.arrow_forwardPerform the following Matrix Operations for the predefined matrices. Given the System of equations: 2х + 4y — 5z + Зw %3D —33 3х + 5у—2z + бw %3D — 37 х — 2у + 4z — 2w 3 25 Зх + 5у-3z + Зw = -28 Write the systems as Ax = b, where A is the coefficient matrix and b is the vector for the constants. 1. Encode the Matrix A and the column vector b. 2. Solve for Determinant of A. 3. Find the Inverse of A. 4. Form the Reduced Row Echelon of A. 5. Find the number of rows and number of columns of Ab. 6. Find the sum of the columns of A. 7. In each of the columns of A, find the highest values and its indices. 8. Augment A with b; 9. Find b\A 10. Form the Reduced Row Echelon of Ab. 11. Extract the Last Column of the Reduced Row Echelon Form of Ab. 12. Create a matrix A whose elements are the same as matrix A, but the first column is the column vector b. 13. Create a matrix A whose elements are the same as matrix A, but the second column is the column vector b. 14. Create a matrix A whose elements…arrow_forward
- Let A be an m × n matrix with m > n. (a) What is the maximum number of nonzero singular values that A can have? (b) If rank(A) = k, how many nonzero singular values does A have?arrow_forwardAssume A is k x n-matrix and P is k × k-invertible matrix. Prove that rank(PA) = rank(A).arrow_forward| IF A = 3 -4 3 0-3 -2 The Cofactor Matrix is :-arrow_forward
- Given a square matrix A that is diagonalizable. Determine whether the matrix is diagonalizable. (It isn't allowed to use any direct command of Matlab or Python to find the eigenvalues and eigenvector of A). Give example for each case.arrow_forwardOrthogonal linear operator : has the standard basis matrix: Find an orthonormal basis in which the operator matrix has a canonical form and write out this matrix. Specify the axis and angle of rotation defined by the operatorarrow_forwardFor the matrix A, find (if possible) a nonsingular matrix P such that p-lAP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -3 A = -2 P = Verify that P1AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP =arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
![Text book image](https://www.bartleby.com/isbn_cover_images/9780534380588/9780534380588_smallCoverImage.gif)
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole