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#include <iostream>
using namespace std;
//Function to determine whether Matrix is Identity or not
bool isIdentityMatrix (int** matrix,int rows, int columns);
bool isOrthogonalMatrix (int** matrix,int rows, int columns);
//Function of Matrices Transpose
int** Matrices_Transpose(int** matrix, int rows, int columns);
int main()
{
int **Matrix1,**Matrix2 ,**Matrix_Result,**transposeMatrix1,**transposeMatrix2 ;
int **Matrix_Multiply; //To dynamically allocate Arrays
bool Matrix_Identity;
int Rows1,Cols1 ,Rows2,Cols2;
//The User input the Rows and the Columns of Matrix 1 and 2
cout<<"Number of Rows of Matrix#1 : ";
cin>>Rows1;
cout<<"Number of Columns of Matrix#1 : ";
cin>>Cols1;
cout<<"Number of Rows of Matrix#2 : ";
cin>>Rows2;
cout<<"Number of Columns of Matrix#2 : ";
cin>>Cols2;
//Allocation of 2D Matrices Arrays
Matrix1= new int*[Rows1];
for(int i=0;i<Rows1;i++){
Matrix1[i]= new int[Cols1];
}
Matrix2= new int*[Rows2];
for(int i=0;i<Rows2;i++){
Matrix2[i]= new int[Cols2];
}
Matrix_Result = new int*[Rows1];
for(int i=0;i<Rows1;i++){
Matrix_Result[i]= new int[Cols2];
}
Matrix_Multiply = new int*[Rows1];
for(int i=0;i<Rows1;i++){
Matrix_Multiply[i]= new int[Cols2];
}
//Filling 2D Matrix#1 Array
cout<<"Matrix #1 : "<<endl;
for(int i=0;i<Rows1;i++)
{
for(int j=0;j<Cols1;j++)
{
cin>>Matrix1[i][j];
}
}
cout<<"Matrix #2 : "<<endl;
for(int i=0;i<Rows2;i++)
{
for(int j=0;j<Cols2;j++)
{
cin>>Matrix2[i][j];
}
}
//--------------------------------------------------------------
//Check Orthogonal Matrix
if(isOrthogonalMatrix(Matrix1,Rows1,Cols1))
cout<<"Matrix #1 is orthogonal "<<endl;
else
cout<<"Matrix #1 is not orthogonal"<<endl;
if(isOrthogonalMatrix(Matrix2,Rows2,Cols2))
cout<<"Matrix #2 is orthogonal "<<endl;
else
cout<<"Matrix #2 is not orthogonal"<<endl;
//---------------------------------------------------------------
//Deallocation of 2D Array
for(int i=0; i<Rows1;i++)
{
delete []Matrix1[i];
}
delete []Matrix1;
for(int i=0; i<Rows2;i++)
{
delete []Matrix2[i];
}
delete []Matrix2;
for(int i=0; i<Rows1;i++)
{
delete []Matrix_Result[i];
}
delete []Matrix_Result;
for(int i=0; i<Rows1;i++)
{
delete []transposeMatrix1[i];
}
delete []transposeMatrix1;
for(int i=0; i<Rows1;i++)
{
delete []transposeMatrix2[i];
}
delete []transposeMatrix2;
return 0;
}
bool isIdentityMatrix (int** matrix,int rows, int columns)
{
bool Matrix_identity=true;
for (int i=0;i<rows;i++)
{
for (int j=0;j<columns;j++)
{
if (i==j&&matrix[i][j]!=1)
{
Matrix_identity=false;
break;
}
else if (i!=j &&matrix[i][j]!=0)
{
Matrix_identity=false;
break;
}
}
if (! Matrix_identity)break;
}
return Matrix_identity;
}
bool isOrthogonalMatrix (int** matrix,int rows, int columns)
{
bool Matrices_Orthogonal = true ;
int ** Result ,**transpose ;
Result = new int*[rows];
transpose= new int*[rows];
for(int i=0;i<rows;i++)
{
Result[i]= new int[columns];
}
for(int i=0;i<rows;i++)
{
transpose[i]= new int[columns];
}
transpose =Matrices_Transpose(matrix,rows,columns);
for (int i=0;i<rows;i++)
{
for (int j=0;j<columns;j++)
{
Result[i][j]=0;
for (int k=0;k<rows;k++)
Result[i][j]+=matrix[i][k]*transpose[k][j];
}
}
if(isIdentityMatrix(Result,rows,columns))
{
for (int i=0;i<rows;i++)
{
for (int j=0;j<columns;j++)
{
Result[i][j]=0;
for (int k=0;k<rows;k++)
Result[i][j]+=transpose[i][k]*matrix[k][j];
}
}
if(isIdentityMatrix(Result,rows,columns))
{
Matrices_Orthogonal = true;
}
}
else
{
Matrices_Orthogonal = false;
}
return Matrices_Orthogonal;
}
int** Matrices_Transpose(int** matrix, int rows, int columns)
{
int ** Result ;
Result = new int*[columns];
for(int i=0;i<columns;i++)
{
Result[i]= new int[rows];
}
for(int i=0;i<rows;i++)
{
for(int j=0;j<columns;j++)
{
Result[j][i] =matrix[i][j];
}
}
return Result;
}
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