线性方程组的矩阵表示_用矩阵表示线性方程组

线性方程组的矩阵表示

A Linear Equation can be represented in matrix form using a:

线性方程可以使用以下形式以矩阵形式表示：

Coefficient Matrix
系数矩阵
Variable Matrix and
可变矩阵和
Constant Matrix
常数矩阵

The System of linear equation in three variables,

由三个变量组成的线性方程组，

a1x+b1y+c1z=d1
a2x+b2y+c2z=d2
a3x+b3y+c3z=d3

The Matrix Representation would be

矩阵表示为

a1 b1 c1       xd1
a2 b2 c2y      =d2
a3 b3 c3 zd3

We generalize the result of n variable

我们推广n变量的结果

a1 b1 c1             
a2 b2 c2     __     Coefficient Matrix
a3 b3 c3
x,y,z  are Variable Matrix
d1,d2,d3 are Constant Matrix

Consider the System,

考虑一下系统

x+2y+3z=4
5x+6y+7z=8
8x+7y+6z=5

Then, the coefficient matrix for the above system is

然后，上述系统的系数矩阵为

1 2 3 
5 6 7 
8 7 6

Variable Matrix are X, Y, Z

变量矩阵是X ， Y ， Z

Constant Matrix are 4,8,5

常数矩阵为4,8,5

Representing of linear Matrix in above System is:

上述系统中线性矩阵的表示为：

1 2 3 x     4
5 6 7 y     = 8
8 7 6 z     5

C ++程序以矩阵形式实现线性方程的表示 (C++ program to implement the Representation of Linear Equation in Matrix form)

#include <iostream>
using namespace std;
int main()
{
cout<< "Enter the number of variables in the equations: ";
int n;
cin>>  n;
char var = 'x';
int a[n][n],b[n][1];
for (int i = 0; i< n; i++)
{
for (int j = 0; j < n; j++)
{
cin>> a[i][j];   //Get the Matrix values
}
cin>> b[i][0]; //Get the constant values
}
cout<< "\nLinear Equation in Matrix representation is: \n";
for (int i = 0; i< n; i++)
{
for (int j = 0; j < n; j++)
{
cout<<" "<< a[i][j]; //print the matrix values
}
//print the variable and constant values
cout<< "  " <<static_cast<char>(var) << "  =  " << b[i][0]<< "\n";
var++;
}
return 0;
}

Output

输出量

Enter the number of variables in the equations:
3
1 2 3 4
5 6 7 8
8 7 6 5
Linear Equation in Matrix representation is: 
1 2 3 x   =    4
5 6 7 y   = 8
8 7 6 z   =   5

Applications:

应用范围：

Systems of Linear Equations can be used to solve some Real – Time Problems:

线性方程组可以用来解决一些实时问题 ：