找到一个3x3矩阵的辅助因子和决定因素（JAVA） [英] finding cofactor and determinant of a 3x3 matrix (java)

问题描述

我计算的产品，和，转（的产品），但我不知道从哪里开始在产品矩阵的辅助因子和行列式。

我见过一对夫妇的例子，但没有一个类似于我特别code，如果任何人能告诉我，我如何将这两种方法纳入我的程序

我倒是高AP preciate它。

请不要问我什么，我已经试过，因为正如我所说，我无言以对的时刻

  //这里是code我写的产品：包programEx;
进口java.io. *;
进口的java.util。*;
进口的java.io.File *。
进口java.util.Scanner中;公共类progEx {    公共静态无效的主要（字串[] args）{
    //建立输入流
       扫描器S =新的扫描仪（System.in）;
       System.out.print（在一个输入行数：）;
       INT rowsInA = s.nextInt（）;
       System.out.print（在A /排在b输入列数：）;
       INT columnsInA = s.nextInt（）;
       System.out.print（输入B中的列数：）;
       INT columnsInB = s.nextInt（）;       INT [] []一个=新INT [rowsInA] [columnsInA];
       INT [] [] B =新INT [columnsInA] [columnsInB]; //以用户输入1矩阵
       的System.out.println（输入矩阵A）;
       的for（int i = 0; I＆LT;则为a.length;我++）{
           为（中间体J = 0; J＆下;一个[0]。长度; J ++）{
               一个[I] [J] = s.nextInt（）;
           }
       }
 //以用户输入第二矩阵
       的System.out.println（输入矩阵B）;
       的for（int i = 0; I＆LT; b.length个;我++）{
           为（中间体J = 0; J＆下; B [0]。长度; J ++）{
               B〔I] [J] = s.nextInt（）;
           }
       } //调用倍增法并将它传递给两个矩阵
       INT [] [] C =乘（A，B）;
       的System.out.println（A的产品，B是）;
       的for（int i = 0; I＆LT; c.length;我++）{
           为（中间体J = 0; J＆c为C [0]。长度; J ++）{
               System.out.print（C [I] [J] +）;           }
           的System.out.println（）;
       }  }//为第一和第二矩阵乘法单独的方法
   公共静态INT [] []乘（INT [] []一，INT [] [] B）{
       INT rowsInA =则为a.length;
       INT columnsInA =一个[0]。长度;
       INT columnsInB = B [0]。长度;
       INT [] [] C =新INT [rowsInA] [columnsInB];
       的for（int i = 0; I＆LT; rowsInA;我++）{
           对于（INT J = 0; J＆LT; columnsInB; J ++）{
               对于（INT K = 0; K＆LT; columnsInA; k ++）{
                   C [I] [J] = C [I] [J] + A [I] [K] * B [k]的[J]。
               }
           }
       }
       返回℃;
   }
}
 

解决方案

好了，一个3 * 3的矩阵有3列和3行的开始。
每始于指数0。

行列式可以计算为：

  INT D =行列式（）;
INT决定（）
{
  INT X = A [0] [0] *（（一[1] [1] *一个[2] [2]） - （一[2] [1] *一个[1] [2]））;
   INT Y = -a [0] [1] *（（一个[0] [1] *一个[2] [2]） - （一[2] [0] *一[1] [2]））;
 INT Z = A [0] [2] *（（一[1] [0] *一个[2] [1]） - （一[1] [1] *一个[2] [0]））;    INT R = X + Y + Z;
    返回ř;
    }
 

这是只为寻找一个3×3矩阵的行列式。

I computed the product, sum, and transpose(of product), but I have no clue where to start on the cofactor and determinent of the product matrix.

Ive seen a couple examples but none that resemble my particular code so if anyone could show me how i could incorporate these two methods into my program I'd high appreciate it.

please dont ask me what i've tried because as I stated I am clueless at the moment

//here is the code I wrote for the product:

package programEx;
import java.io.*;
import java.util.*;
import java.io.File.*;
import java.util.Scanner;

public class progEx {

    public static void main(String[] args) {
    //Establishing Input Stream
       Scanner s = new Scanner(System.in);
       System.out.print("Enter number of rows in A: ");
       int rowsInA = s.nextInt();
       System.out.print("Enter number of columns in A / rows in B: ");
       int columnsInA = s.nextInt();
       System.out.print("Enter number of columns in B: ");
       int columnsInB = s.nextInt();

       int[][] a = new int[rowsInA][columnsInA];
       int[][] b = new int[columnsInA][columnsInB];

 //Taking user input for 1st matrix
       System.out.println("Enter matrix A");
       for (int i = 0; i < a.length; i++) {
           for (int j = 0; j < a[0].length; j++) {
               a[i][j] = s.nextInt();
           }
       }
 //Taking user input for 2nd matrix
       System.out.println("Enter matrix B");
       for (int i = 0; i < b.length; i++) {
           for (int j = 0; j < b[0].length; j++) {
               b[i][j] = s.nextInt();
           }
       }

 //calling the multiplication method and passing it to both matrices
       int[][] c = multiply(a, b);
       System.out.println("Product of A and B is");
       for (int i = 0; i < c.length; i++) {
           for (int j = 0; j < c[0].length; j++) {
               System.out.print(c[i][j] + " ");

           } 
           System.out.println();
       } 

  }

//Separate method for the multiplication of 1st and 2nd matrices
   public static int[][] multiply(int[][] a, int[][] b) {
       int rowsInA = a.length;
       int columnsInA = a[0].length; 
       int columnsInB = b[0].length;
       int[][] c = new int[rowsInA][columnsInB];
       for (int i = 0; i < rowsInA; i++) {
           for (int j = 0; j < columnsInB; j++) {
               for (int k = 0; k < columnsInA; k++) {
                   c[i][j] = c[i][j] + a[i][k] * b[k][j];
               }
           }
       }
       return c;
   }
}

解决方案

Well,a 3*3 matrix has 3 columns and 3 rows to begin with. Each starts with an index 0.

Determinant can be calculated as:

int d=determinant();
int determinant()
{
  int x=a[0][0]*((a[1][1]*a[2][2])-(a[2][1]*a[1][2]));
   int y=-a[0][1]*((a[0][1]*a[2][2])-(a[2][0]*a[1][2]));
 int z=a[0][2]*((a[1][0]*a[2][1])-(a[1][1]*a[2][0]));

    int r=x+y+z;
    return r;
    }

This is only for finding the determinant of a 3*3 matrix.

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