Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Expert Solution & Answer
Chapter 2.5, Problem 8P
Explanation of Solution
a.
Inverse of the given matrix:
We know that for any square matrix
Therefore, we have,
Hence, we get
Explanation of Solution
b.
Obtaining the inverse:
Suppose
Then we have,
Now, we have,
Explanation of Solution
c.
Obtaining the inverse:
Suppose
Then, we have,
Now, we have,
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these 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.
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
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…
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
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Chapter 2 Solutions
Introduction to mathematical programming
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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