Question

Given two 2-dimensional arrays, A and B, calculate the three arrays: A + B, A*B and A*B^-1 . That is to say find the sum of the two arrays, the outer-product of the two arrays and the outer-product of A times B inverse.

You can use the procedure illustrated on the web site:

https://www.thecrazyprogrammer.com/2017/02/c-c-program-find-inverse-matrix.html (Links to an external site.)

• make the arrays 3X3, choose any values you wish
• make sure the determinant of B is not zero, if so change the values in B.
• when you run the inverse program from the website listed it will tell you if the determinant is zero.
• add the output to the end of the .cpp file.
• add a comment on the calculation of the inverse array.

Answer 1

C++ Program:

#include <iostream>
#include <iomanip>

using namespace std;

//Printing matrix
void printMatrix(double res[3][3])
{
int i, j;

cout << fixed << setprecision(2);

//Iterating over rows
for(i=0; i<3; i++)
{
//Iterating over columns
for(j=0; j<3; j++)
{
cout << left << setw(6) << res[i][j] << " ";
}

cout << "\n";
}
}

//Matrix Addition
void matrixAddition(double mat1[3][3], double mat2[3][3], double res[3][3])
{
int i, j;

//Iterating over rows
for(i=0; i<3; i++)
{
//Iterating over columns
for(j=0; j<3; j++)
{
res[i][j] = mat1[i][j] + mat2[i][j];
}
}
}

//Matrix Multiplication
void matrixMultiplication(double mat1[3][3], double mat2[3][3], double res[3][3])
{
int i, j, k;

//Iterating over rows
for(i=0; i<3; i++)
{
//Iterating over columns
for(j=0; j<3; j++)
{
res[i][j] = 0;

for(k=0; k<3; k++)
{
res[i][j] += mat1[i][k] + mat2[k][j];
}
}
}
}

void inverse(double mat[3][3], double res[3][3])
{
int i, j;
double det=0;

//finding determinant
   for(i = 0; i < 3; i++)
{
det = det + (mat[0][i] * (mat[1][(i+1)%3] * mat[2][(i+2)%3] - mat[1][(i+2)%3] * mat[2][(i+1)%3]));
}

cout << "\n\n Determinant: " << det << "\n\n";

   for(i = 0; i < 3; i++)
{
       for(j = 0; j < 3; j++)
       {
res[i][j] = ((mat[(j+1)%3][(i+1)%3] * mat[(j+2)%3][(i+2)%3]) - (mat[(j+1)%3][(i+2)%3] * mat[(j+2)%3][(i+1)%3]))/(double)det;
       }
}
}

//Main function
int main()
{
//Declaring arrays
double A[3][3] = {{1, 2, 3},{4, 5, 6},{7, 8, 9}};
double B[3][3] = {{3, 0, 2},{2, 0, -2},{0, 1, 1}};
double C[3][3];
double BInv[3][3];

cout << "\n\n Matrix A: \n\n";
printMatrix(A);

cout << "\n\n Matrix B: \n\n";
printMatrix(B);

//Addition
matrixAddition(A, B, C);

cout << "\n\n Matrix C = A+B: \n\n";
printMatrix(C);

//Multiplication
matrixMultiplication(A, B, C);

cout << "\n\n Matrix C = A*B: \n\n";
printMatrix(C);

//Inverse
inverse(B, BInv);

cout << "\n\n Matrix B-1: \n\n";
printMatrix(BInv);

matrixMultiplication(A, BInv, C);

cout << "\n\n Matrix C = A+B-1: \n\n";
printMatrix(C);

cout << "\n\n";
return 0;
}

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Sample Run: