Represent Linear Equations in Matrix Form using Java

In this segment of Java programming, we are going to learn and discover certain programs by which we can represent linear equations in Matrix form. To do these programs, we first have to learn about linear equations and Matrix forms, their types, and how they are solved by simple mathematical methods.

We will learn how to integrate a scanner class of java.util package to take input from the user using Java build code. The array will initialize to store some variables as input for the problem matrix. Then, it will be converted into a loop by which the problem equation will be solved. 

What Is a Linear Equation?

A linear equation is a type of equation in which the highest power of a variable is 1, which is also known as a one-degree equation.

There are 3 major types of linear equations ?

• Point slope form

• Standard form

• Slope intercept form

Certain methods, such as elimination, substitution, cross multiplication, and matrix, can be used to solve linear equations.

What Is a Matrix in the View of Java Environment?

A matrix is the arrangement of given numbers in rows and columns. It depends on how many rows and columns are present in the given set. These can have different integers, variables, a combined form of either of them or some special letters like alpha, beta, gamma, etc.

There are so many types of matrix forms ?

• row matrix

• column matrix

• null matrix

• square matrix

• diagonal matrix

• upper triangular matrix

• lower triangular matrix

• symmetric matrix

• antisymmetric matrix

Steps to Represent Linear Equation

Following are the steps to represent the linear equation in matrix form ?

• Step 1 ? Generate a scanner class for programming

• Step 2 ? take three different variables

• Step 3 ? Putting all the calculations and formations one by one

• Step 4 ? print all the variables and integers in S.O.P

• Step 5 ? close the program with the scanner class system at the end and then compile the program.

Syntax

data_type[The Dimension][The Dimension].....[Nth number of dimension] 
array_name = new data_type[Size of data][size of data].......[size of data at Nth Position];

This sequence of equations and Matrix is set up differently in the Java language. We have to insert a program in which input will be given in linear equations and output will be in Matrix format or vice versa. To do these we have to go through many examples and steps in the following ?

Conduct the linear equations for the 3 coefficients

For an example a representation is also shown below:-

System of Linear Equation

3x + 5y + 8z = 24

8x + 10y + 12z = 30

2x + 4y + 5z = 5

Matrix representation

      3.   5.   8                  x                           24
 A =  8.  10.  12            X =   y                   B  =    30
      2.   4.   5.                 z                            5

For a better understanding of representing the linear equations in Matrix form, we have provided a program to learn this set of coding below -

Example 1

import java.util.Scanner;

public class matrix07tutorialspoint {
	public static void main(String args[]){
      
      System.out.println("###### 3 variable linear equation ######");	
      char[] variable = { 'x', 'y', 'z' };
      Scanner sc = new Scanner(System.in);	
      System.out.println("Enter input as the coefficients of 3 variable");
      System.out.println("Enter in the specific format shown");
      System.out.println("ex + fy + gz = j");
      int[][] matrix = new int[3][3];
      int[][] constt = new int[3][1];

      
      for (int k = 0; k < 3; k++) {
      	
         for (int j = 0; j < 3; j++) {      
            matrix[k][j] = sc.nextInt();
      	 }	
      	 constt[k][0] = sc.nextInt();
      }
      System.out.println("Matrix representation of above linear equations is: ");
      for (int k = 0; k < 3; k++) {	
         for (int j = 0; j < 3; j++) {      
            System.out.print(" " + matrix[k][j]);
      	 }

      	 System.out.print(" " + variable[k]);
      	 System.out.print(" = " + constt[k][0]);
      	 System.out.println();
      }
      sc.close();
   }
}

Output

###### 3 variable linear equation ######
Enter input as the coefficients of 3 variable
Enter in the specific format shown
ex + fy + gz = j
Exception in thread "main" java.util.NoSuchElementException
	at java.base/java.util.Scanner.throwFor(Scanner.java:941)
	at java.base/java.util.Scanner.next(Scanner.java:1598)
	at java.base/java.util.Scanner.nextInt(Scanner.java:2263)
	at java.base/java.util.Scanner.nextInt(Scanner.java:2217)
	at matrix07tutorialspoint.main(matrix07tutorialspoint.java:20)

Example 2

import java.util.Scanner;

public class ARBRDDTutorialpoint {
   public static void main(String args[]){
      System.out.println("====== n variable of a linear equation ======");
      
      char[] variable= { 'e', 'f', 'g', 'x', 'y', 'z', 'v' };
      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 as we need to perform");
      System.out.println("To get the result enter the input in the format shown below");
      System.out.println("ex + fy + gz + ... = o");
	
      
      int[][] matrix = new int1[num][num];
      int[][] constt = new int1[num][1];
      for (int k = 0; k < num; k++) {
         for (int j = 0; j < num; j++) {
            matrix[k][j] = sc.nextInt();
      	 }
      	 constt[k][0] = sc.nextInt();
      }
      
      System.out.println("Matrix representation of above linear equations are: ");
      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

====== n variable of a linear equation ======
Enter the number of variables
4
Enter the coefficients variable as we need to perform
To get the result enter the input in the format shown below
ex + fy + gz + ... = o
10 11 12 13
14 15 16 16
18 19 20 21
22 23 24 25

--------OUTPUT INCOMPLETE ------- PLEASE CHECK--------------