Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
Expert Solution & Answer
Book Icon
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 A of order n×n having elements aij and another matrix B of same order having elements bij.

Now, the addition of these matrices is,

A+B=[aij+bij]

The trace of this matrix is given below:

trace(A+B)=i=1n[aii+bii]

We can write this as follows:

  

Explanation of Solution

b.

Proof:

Consider any n×n matrices A and B.

Suppose C=AB.

Then the elements of this matrix are cij.

Then we can write,

cij=k=1n[aikbkj]

Similarly, let D=BA.

Then the elements of this matrix are dij.

Then we can write,

dij=k=1n[bikakj]

Now, the trace of the matrix AB is given below:

trace(AB)=i=1ncii

      =i=1n(k=1naikbki<

Blurred answer
Students have asked these similar questions
I want to solve 13.2 using matlab please help
a) Show a possible trace of the OSPF algorithm for computing the routing table in Router 2 forthis network.b) Show the messages used by RIP to compute routing tables.
using r language to answer question 4 Question 4: Obtain a 95% standard normal bootstrap confidence interval, a 95% basic bootstrap confidence interval, and a percentile confidence interval for the ρb12 in Question 3.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole
Text book image
C++ for Engineers and Scientists
Computer Science
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Course Technology Ptr