Question

(In Java) An n X n matrix is called a positive Markov matrix if each element is positive and the sum of the elements in each column is 1. Write the following method to check whether a matrix is a Markov matrix.
public static boolean isMarkovMatrix(double[][] m)
Write a test program that prompts the user to enter a 3 X 3 matrix of double values and tests whether it is a Markov matrix.
Sample run:
Enter a 3-by-3 matrix row by row:
0.15 0.875 0.375
0.55 0.005 0.225
0.30 0.12 0.4
It is a Markov matrix

Answer 1

Answer:

In Java:

import java.util.*;

public class Main{

public static void main(String[] args) {

 Scanner input = new Scanner(System.in);

 System.out.print("Enter a 3 x 3 matrix: ");

 double[][] myArr = new double[3][3];

 for(int i =0;i<3;i++){

        for(int j = 0;j<3;j++){

         myArr[i][j] = input.nextDouble();}}

 boolean isMarkov = true;

 double colsum = 0.00;

 for(int i =0;i<3;i++){

     for(int j = 0;j<3;j++){

         colsum += myArr[j][i];}

     if(colsum != 1.00){

         isMarkov = false;

         break;}

     colsum = 0.00;

 }

 if(isMarkov){    System.out.print("It is a Markov matrix"); }

 else{  System.out.print("It is a not Markov matrix"); }

}

}

Explanation:

This line prompts the user for a $3\ x\ 3$ matrix

 System.out.print("Enter a $3\ x\ 3$ matrix: ");

This declares a 3 x 3 matrix

 double[][] myArr = new double[3][3];

The following iteration gets input for the $3\ x\ 3$ matrix

 for(int i =0;i<3;i++){

        for(int j = 0;j<3;j++){

         myArr[i][j] = input.nextDouble();}}

This declares and initializes a boolean variable to true

 boolean isMarkov = true;

This declares and initializes colsum to 0 i.e. the sum of each column

 double colsum = 0.00;

The following iteration sums up each column

 for(int i =0;i<3;i++){

     for(int j = 0;j<3;j++){

         colsum += myArr[j][i];}

This checks if the column sum is not 1

     if(colsum != 1.00){

If true that the column sum is not 1, the boolean variable is updated to false

         isMarkov = false;

And the loop is terminated

        break;}

     colsum = 0.00;

 }

If isMarkov is true, the system prints that it is a Markov matrix

 if(isMarkov){    System.out.print("It is a Markov matrix"); }

If isMarkov is false, the system prints that it is not a Markov matrix

 else{  System.out.print("It is a not Markov matrix"); }