行列式求解

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二階行列式求解

有線性代數的知識可知，二階行列式可由對角線法則求解：

$A = [a 11 a 12 a 21 a 22]$
$d e t A = a 11 a 22 - a 21 a 12$

/* * This program about the solution of determinant; * @version 1.01 2017-09-13 * @author huangzihan */package determinant_solve;import java.util.Scanner;public class Determinant_solve {       public static void main(String[] args)       {           int []a=new int[4];           Scanner in=new Scanner(System.in);           System.out.println("請從左往右，從上往下依次輸入行列式的相應數字：");           for(int i=0;i<4;i++)           {               a[i]=in.nextInt();           }           int det=a[0]*a[3]-a[1]*a[2];           System.out.println("det="+det);       }}

三階行列式求解

三階行列式同樣也可以由對角線法則進行求解：

$A = ⎡ ⎣ ⎢ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ⎤ ⎦ ⎥$
$d e t A = a 11 a 22 a 33 + a 21 a 32 a 13 + a 31 a 12 a 23 - a 31 a 22 a 13 - a 11 a 32 a 23 - a 33 a 12 a 21$

/* * This program about the solution of determinant; * @version 1.01 2017-09-13 * @author huangzihan */package determinant_solve;import java.util.Scanner;public class Determinant_solve {       public static void main(String[] args)       {           int []a=new int[9];           Scanner in=new Scanner(System.in);           System.out.println("請從左往右，從上往下依次輸入行列式的相應數字：");           for(int i=0;i<9;i++)           {               a[i]=in.nextInt();           }           int det=a[0]*a[4]*a[8]+a[1]*a[5]*a[6]+a[2]*a[3]*a[7]-a[2]*a[4]*a[6]-a[5]*a[7]*a[0]-a[1]*a[3]*a[8];           System.out.println("det="+det);       }}

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