Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 2.1, Problem 7P
Explanation of Solution
a.
Trace of the given matrix:
The trace of a matrix is the sum of its diagonal elements.
Now, consider a matrix
Now, the addition of these matrices is,
The trace of this matrix is given below:
We can write this as follows:
Explanation of Solution
b.
Proof:
Consider any
Suppose
Then the elements of this matrix are
Then we can write,
Similarly, let
Then the elements of this matrix are
Then we can write,
Now, the trace of the matrix
Expert Solution & Answer
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Perform 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
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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…
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
The meet of two zero-one matrices A and B is described as
AAB = [ajj A bj]
AvB = [aj A bijl]
A v B = [aj v bijl
A AB = [aj v bijl]
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
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