Question

Asked Sep 25, 2019

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Assignment (Math application):

Write a program that prompts the user to enter a 3 x 3 matrix of double values and tests

whether it is a positive Markov matrix.

An n x n matrix is a positive Markov matrix if the following is true:

o If each of the elements is positive

o The sum of the elements in each column is 1

Sample Program running

Enter a 3 x 3 matrix by row

0.15 0.875 0.375

0.55 0.005 0.225

0.30 0.12 0.4

The sum of the columns

1.0 1.0 1.0

It is a Markov matrix

Enter a 3 x 3 matrix by row

-0.2 0.875 0.375

0.75 0.005 0.225

0.45 0.12 0.4

The sum of the columns

1.0 1.0 1.0

It is not a Markov matrix

Please note the following requirements:

Include a comment before each method explaining what the methods will do

All methods called from the main methods

There will be two methods which will be called from the main method:

public static double [] [] createArray()

1. Creates a 3 by 3 two dimensional array of doubles

2. Prompts the user for values as shown in the sample run

3. Stores the numbers in the array in the order entered

4. Returns the array to the main method

public boolean isMarkovMatrix(double [][] matrix)

1. Returns false if any value in the array is negative

2. Prints the sum of each column in the array

3. Returns false if any the sum of any of the columns is not equal to 1.0

4. Otherwise, it returns true.

The program must work correctly for all values (not just the values in the sample

output).

Step 1

**Program Instructions:**

- In main method, call methods createArray() and isMarkovMatrix().
- In method createArray, create a 3*3 array and use scanner class object to get the user input.
- In method isMarkovMatrix(), traverse the array and check for negative values. In the same loop, save the sum of columns in the variable sum and print the sum.

Step 2

**Program:**

import java.util.Scanner;

public class MarkovMatrix {

/** Main method */

public static void main(String[] args) {

// Generate a 3 x 3 matrix of user input

double[][] matrix = createArray();

// Test if matrix is a Markov matrix

System.out.println("\nIt is" + (isMarkovMatrix(matrix) ? " " : " not ") +

"a Markov matrix");

}

/** getMatrix return a 3-by-3 matrix filled with user input */

public static double[][] createArray() {

// Create a Scanner

Scanner input = new Scanner(System.in);

// Create a 3-by-3 matrix

double[][] m = new double[3][3];

// Prompt ther user to enter a 3 x 3 matrix

System.out.println("Enter a 3 x 3 matrix by row");

for (int i = 0; i < m.length; i++) {

for (int j = 0; j < m[i].length; j++) {

m[i][j] = input.nextDouble();

}

}

return m;

}

&nb...

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