Let’s look at the System of Linear Equation with the help of an example:
The input of coefficients and variables is taken into play for consideration.
- The scanner package should be imported into the program in order to use the object of the Scanner class to take the input from the user.
- The array will be initialized to store the variables of the equations.
- The coefficients of the variables will be taken from the user with the help of the object of the Scanner class.
- The equations will then converted into the form of a matrix with the help of a loop.
Two examples are laid off:
- 3 variable linear equations in matrix form.
- N variable linear equations in matrix form.
Illustration: Considering the most used practical linear equation used in mathematics, that is 3 variable linear equations.
Input: ax + by + cz = d
Output - 1 2 3 x = 10
5 1 3 y = 12
7 4 2 z = 20
Example 1: Java Program for 3 variable linear equations in matrix form.
Java
// Java Program to Represent Linear Equations in Matrix Form// Importing Scanner class// to take input from userimport java.util.Scanner;public class GFG { // Mai driver method public static void main(String args[]) { // Display message for better readability System.out.println( "******** 3 variable linear equation ********"); // 3 variables of the linear equation char[] variable = { 'x', 'y', 'z' }; // Creating Scanner class object Scanner sc = new Scanner(System.in); // Display message for asking user to enter input System.out.println( "Enter the coefficients of 3 variable"); System.out.println( "Enter in the format shown below"); System.out.println("ax + by + cz = d"); // For 3*3 matrix or in other words // Dealing with linear equations of 3 coefficients // Input of coefficients from user int[][] matrix = new int[3][3]; int[][] constt = new int[3][1]; // Outer loop for iterating rows for (int i = 0; i < 3; i++) { // Inner loop for iterating columns for (int j = 0; j < 3; j++) { // Reading values from usr and // entering in the matrix form matrix[i][j] = sc.nextInt(); } // One row input is over by now constt[i][0] = sc.nextInt(); } // The linear equations in the form of matrix // Display message System.out.println( "Matrix representation of above linear equations is: "); // Outer loop for iterating rows for (int i = 0; i < 3; i++) { // Inner loop for iterating columns for (int j = 0; j < 3; j++) { // Printing matrix corresponding // linear equation System.out.print(" " + matrix[i][j]); } System.out.print(" " + variable[i]); System.out.print(" = " + constt[i][0]); System.out.println(); } // Close the stream and release the resources sc.close(); }} |
Output:
Now, getting it generic for any value of N: “n-variable linear equation”
Illustration:
Input: ax + by + cz + ... = d
Output: 1 2 3 x = 10
5 1 3 y = 12
7 4 2 z = 20
...
...
Example 2: Java Program for N variable linear equations in matrix form.
Java
import java.util.Scanner;public class Linear_Equations_n { public static void main(String args[]) { System.out.println( "******** n variable linear equation ********"); // Initializing the variables char[] variable = { 'a', 'b', 'c', 'x', 'y', 'z', 'w' }; System.out.println("Enter the number of variables"); Scanner sc = new Scanner(System.in); int num = sc.nextInt(); System.out.println( "Enter the coefficients variable"); System.out.println( "Enter in the format shown below"); System.out.println("ax + by + cz + ... = d"); // Input of coefficients from user int[][] matrix = new int[num][num]; int[][] constt = new int[num][1]; for (int i = 0; i < num; i++) { for (int j = 0; j < num; j++) { matrix[i][j] = sc.nextInt(); } constt[i][0] = sc.nextInt(); } // Representation of linear equations in form of // matrix System.out.println( "Matrix representation of above linear equations is: "); for (int i = 0; i < num; i++) { for (int j = 0; j < num; j++) { System.out.print(" " + matrix[i][j]); } System.out.print(" " + variable[i]); System.out.print(" = " + constt[i][0]); System.out.println(); } sc.close(); }} |
Output –
4 – variable linear equations
5 – variable linear equations
Time Complexity: O(N2)
Auxiliary Space: O(N2)
The extra space is used to store the elements in the matrix.
