This is the Java Program to Find the Modulus of a Matrix.Problem Description
Given a square matrix, find and print the modulus(determinant) of the matrix.
Example:
Matrix:
1 2 3
4 5 6
7 8 9
Output:
Modulus = 0Problem Solution
The algorithm for calculating modulus of 3*3 matrix is
x=(matrix[0][0] * (matrix[1][1] * matrix[2][2] – matrix[1][2] * matrix[2][1]));
y=(matrix[0][1] * (matrix[1][0] * matrix[2][2] – matrix[1][2] * matrix[2][0]));
z=(matrix[0][2] * (matrix[1][0] * matrix[2][1] – matrix[1][1] * matrix[2][0]));
determinant= x – y + z;Program/Source Code
Here is the source code of the Java Program to Find the Modulus of a Matrix. The program is successfully compiled and tested using IDE IntelliJ Idea in Windows 7. The program output is also shown below.
//Java Program to Find the Modulus of a import java.io.BufferedReader; import java.io.InputStreamReader; public class ModulusOfAMatrix { // Function to read array elements and calculate the determinant public static void main(String[] args) { BufferedReader br= new BufferedReader(new InputStreamReader(System.in)); int order=3; int[][] matrix=new int[3][3]; System.out.println("Enter the elements of 3x3 matrix"); int i,j; for(i=0;i<matrix.length;i++){ for(j=0;j<matrix[i].length;j++){ try{ matrix[i][j]=Integer.parseInt(br.readLine()); } catch(Exception e){ System.out.println("An error occured. Please retry"); return; } } } int determinant,x,y,z; x=(matrix[0][0] * (matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1])); y=(matrix[0][1] * (matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0])); z=(matrix[0][2] * (matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0])); determinant= x - y + z; System.out.println("The modulus of the given matrix is "+ determinant); } }
Program Explanation
1. In function main(), a matrix is entered.
2. Then in variables x, y and z various coefficients are calculated.
3. Finally, the statement (determinant= x – y + z), calculates the determinant and it is displayed.
Time Complexity: O(1).Runtime Test Cases
Case 1 (Simple Test Case): Enter the elements of 3x3 matrix 1 2 3 4 5 6 7 8 9 The modulus of the given matrix is 0 Case 2 (Simple Test Case - another example): Enter the elements of 3x3 matrix 12 43 5 23 56 7 45 2 65 The modulus of the given matrix is -19598