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#include<iostream>
using namespace std;
int main()
{
int add(int matA[3][3],int matB[3][3]);
int sub(int matA[3][3],int matB[3][3]);
int mul(int matA[3][3],int matB[3][3]);
int Tr(int matA[3][3]);
int det(int matA[3][3]);
int Trans(int matA[3][3]);
int cofactor(int mat[3][3]);
int inv(int matA[3][3]);
int solve(int matA[3][3],int b[3]);
int x,A[3][3],B[3][3],b[3],C[3][3];
cout<<"This program allows you to perform certain matrix and vector operations on a 3x3 matrix"<<endl;
cout<<"If you wish to add two matrices, subtract one matrix from another one, multiply two matrices, calculate the trace, the determinant, transpose, adjoint, inverse or solve a linear system of equations, press 1,2,3,4,5,6,7,8 or 9, respectively";
cin>>x;
switch(x){
case 1:
{
cout<<"enter matrix 1";
cin>>A[3][3];
cout<<"enter matrix 2";
cin>>B[3][3];
cout<<"the sum is "<<add(A,B);
break;
}
case 2:
{
cout<<"enter matrix 1";
cin>>A[3][3];
cout<<"enter matrix 2";
cin>>B[3][3];
cout<<"the difference is"<<sub(A,B);
break;
}
case 3:
{
cout<<"enter matrix 1";
cin>>A[3][3];
cout<<"enter matrix 2";
cin>>B[3][3];
cout<<"the product is"<<mul(A,B);
break;
}
case 4:
{
cout<<"enter your matrix";
cin>>A[3][3];
cout<<"the trace is "<<Tr(A);
break;
}
case 5:
{
cout<<"enter your matrix";
cin>>A[3][3];
cout<<"the determinant is"<<det(A);
break;
}
case 6:
{
cout<<"Enter your matrix";
cin>>A[3][3];
cout<<"The transpose is"<<Trans(A);
break;
}
case 7:
{
cout<<"Enter your matrix";
cin>>A[3][3];
cout<<"The adjoint is"<<Trans(cofactor(A));
break;
}
case 8:
{
cout<<"Enter your matrix";
cin>>A[3][3];
cout<<"The inverse is"<<inv(A);
break;
}
case 9:
{
cout<<"Do you want to solve an equation in the form Ax=b?" <<endl;
cout<<"Enter your matrix A";
cin >>A[3][3];
cout<<"Enter your vector b";
cin>>b[3];
cout<<"The solution is"<<inv(A)*b[3];
break;
}
default:
{
cout<<"Choose a number between 1 and 9 inclusive";
}
}
int add(int matA[3][3],int matB[3][3]);
{
for(int i=0;i<3;i++)
{
for(int j=0;j<3;j++)
{
return A[i][j]+B[i][j];
}
}
}
int sub(int matA[3][3],int matB[3][3]);
{
for (int i=0;i<3;i++)
{
for(int j =0;j<3;j++)
{
return A[i][j]-B[i][j];
}
}
}
int mul (int matA[3][3],int matB[3][3],int matC[3][3]);
{
int i;int j;int k;
for (int i=0; i<3;i++)
for (int j=0;j<3;j++)
for (int k=0;k<3;k++)
C[i][j]=0;
C[i][j]+=A[i][k]*B[k][j];
{
return C[i][j];
}
}
int Tr(int matA[3][3]);
{ return A[0][0]+A[1][1]+A[2][2];
}
int det(int matA[3][3]);
{
return (A[0][0]*((A[1][1]*A[2][2])-(A[1][2]*A[2][1])))-(A[0][1]*((A[1][0]*A[2][2])-(A[1][2]*A[2][0]))+(A[0][2]*((A[1][0]*A[2][1])-(A[1][1]*A[2][0]))));
}
int Trans(int matA[3][3]);
{
int i;int j;
for (int i=0;i<3;i++)
for(int j=0;j<3;j++)
B[i][j]=A[j][i];
return B[i][j];
}
int cofactor(int matB[3][3]);
{
return;
{
C[0][0]=B[1][1]*B[2][2]-B[2][1]*B[1][2];
C[0][1]=-(B[1][0]*B[2][2]-B[2][0]*B[1][2]);
C[0][2]=B[1][0]*B[2][1]-B[2][0]*B[1][1];
C[1][0]=-(B[0][1]*B[2][2]-B[2][1]*B[0][2]);
C[1][1]=B[0][0]*B[2][2]-B[2][0]*B[0][2];
C[1][2]=-(B[0][0]*B[2][1]-B[2][0]*B[0][1]);
C[2][0]=B[0][1]*B[1][2]-B[1][1]*B[0][2];
C[2][1]=-(B[0][0]*B[1][2]-B[1][0]*B[1][2]);
C[2][2]=B[0][0]*B[1][1]-B[1][0]*B[0][1];
}
}
int inv(int matA[3][3]);
{if (det<=0)
cout<<"the inverse does not exist";
else return (Trans(cofactor(A)))/det;
}
int solve(int matA[3][3],int vectb[3]);
{
return inv(A)*b[3];
}
system("PAUSE");
}
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