以矩阵形式表示线性方程的Java程序

让我们借助一个例子来看看线性方程组：

系数和变量的输入被考虑在内。

1. 应该将扫描仪包导入到程序中，以便使用 Scanner 类的对象来获取用户的输入。
2. 数组将被初始化以存储方程的变量。
3. 将在 Scanner 类对象的帮助下从用户那里获取变量的系数。
4. 然后在循环的帮助下，方程将转换为矩阵的形式。

下岗两个例子：

1. 矩阵形式的 3 个变量线性方程。
2. N个矩阵形式的变量线性方程。

说明：考虑到数学中最常用的实用线性方程，即 3 个变量线性方程。

Input: ax + by + cz = d

Output - 1 2 3 x = 10
     5 1 3 y = 12
      7 4 2 z = 20

示例 1：用于矩阵形式的 3 个变量线性方程的Java程序。

Java

// Java Program to Represent Linear Equations in Matrix Form
 
// Importing Scanner class
// to take input from user
import 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();
    }
}

输出：

现在，让它对任何 N 值通用：“n 变量线性方程”

插图：

Input: ax + by + cz + ... = d

Output: 1 2 3 x = 10
        5 1 3 y = 12
     7 4 2 z = 20
     ...
     ...

示例 2：用于矩阵形式的 N 个变量线性方程的Java程序。

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();
    }
}

输出 -

4 – 可变线性方程

5 – 可变线性方程