Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
4th Edition
ISBN: 9780534423551
Author: Wayne L. Winston
Publisher: Cengage Learning
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Expert Solution & Answer
Chapter 2.1, Problem 4P
Explanation of Solution
Proving
Consider a matrix A of order
Thus, the matrix AB will be of the order
The matrix A has elements
Then, the element of D=AB will be of the form given below:
Transpose of this matrix is
And the element of the matrix
Now the transpose of the matrix B is
The element in
Expert Solution & Answer
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3
: Prove that the sum of the three variables of the sum exponent f(x) = Σe is strictly convex. For this
i=1
purpose, compute the Hessian matrix of the function f(x).
(Cayley-IHamilton Theorem) The Cayley-Ilamilton theorem is a powerful theorem in
Linear algebra that states: every square matrix of real numbers satisfies its own char-
acteristic equation. For 2 x 2 matrices this can be seen in the following way. First, we
introduce the trace of the matrix
tr A
41,1 +22
and the determinant
det A = a11a22 - 41,22,1-
Then, the chacteristic polynomial is the quadratic given by
p(A) = x – (tr A)A + (det. A).
Then, for any 2 x 2 matrix, if you plug it into this polynomial, you should always get
a zero matrix.
c_h_test Function:
Input parameters:
• a single 2 x2 matrix for which you would like to test the Cayley Ilamilton
Theorem
Local Variables:
• two scalars to represent the trace and determinant
Output parameters:
a single 2 x2 which is the result of evaluating the charcteristic polynomial
at A (note: think carefully about the constant term)
A possible sample case is:
> mat_B = c_h_test([3, 2 ; 2, 0])
mat B =
0 0
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
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