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Introduction To C++ Programming - Part 4.

C++ Program To Calculate Determinant Of A Matrix
#include<iostream>
#include<math.h>
using namespace std;

double d = 0;
double det(int n, double mat[10][10]);
double det(int n, double mat[10][10]){
double submat[10][10];

if (n == 2) // set the matrix (must be square) to find determinant.
return ((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));

else {
for (int c = 0; c < n; c++) {

int subi = 0;
for (int i = 1; i < n; i++) {

int subj = 0;
for (int j = 0; j < n; j++) {

if (j == c)
continue;

submat[subi][subj] = mat[i][j];
subj++;
}
subi++;
}
d = d + (pow(-1, c) * mat[0][c] * det(n - 1, submat));
}}
return d;
}

int main(int argc, char **argv) {
int n;
double mat[10][10];

cout << "Dimension Of The Matrix: ";
cin >> n;
cout << "\nEnter The Matrix Elements: \n";

for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cin >> mat[j][i];
}}
cout << "\nThe Determinant Of The Above Matrix = " << det(n, mat);
return 0;
}

C++ Program To Find The Adjoint And Inverse Of A Matrix
#include<bits/stdc++.h>
using namespace std;
#define N 3

void getCofactor(int A[N][N], int temp[N][N], int p, int q, int n) {
int i = 0, j = 0;

for (int row = 0; row < n; row++) {
for (int col = 0; col < n; col++) {
if (row != p && col != q) {
temp[i][j++] = A[row][col];

if (j == n - 1) {
j = 0;
i++;
}}}}}

int determinant(int A[N][N], int n) {
int D = 0;
if (n == 1)
return A[0][0];

int temp[N][N];
int sign = 1;

for (int f = 0; f < n; f++) {
getCofactor(A, temp, 0, f, n);
D += sign * A[0][f] * determinant(temp, n - 1);

sign = -sign;
}
return D;
}

void adjoint(int A[N][N],int adj[N][N]) {
if (N == 1) {
adj[0][0] = 1;
return;
}

int sign = 1, temp[N][N];

for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
getCofactor(A, temp, i, j, N);

sign = ((i+j)%2==0)? 1: -1;
adj[j][i] = (sign)*(determinant(temp, N-1));
}}}

bool inverse(int A[N][N], float inverse[N][N]) {
int det = determinant(A, N);

if (det == 0) {
cout << " Singular Matrix, Can't Find Its Inverse.\n";
return false;
}

int adj[N][N];
adjoint(A, adj);

for (int i=0; i<N; i++)
for (int j=0; j<N; j++)
inverse[i][j] = adj[i][j]/float(det);

return true;
}

template<class T>
void display(T A[N][N]) {

for (int i=0; i<N; i++) {
for (int j=0; j<N; j++)
cout << A[i][j] << " ";
cout << endl;
}}

int main() {
int A[N][N],i,j;

cout<<"***  Adjoint & Inverse Of A 3x3 Matrix  *** \n";
cout<<"\nEnter 9 Numbers: \n";

for(i=0;i<N;i++) {
for(j=0;j<N;j++) {
cin >> A[i][j];
}}

int adj[N][N];
float inv[N][N];

cout << "\nInput Matrix:\n";
display(A);

cout << "\nAdjoint Of The Matrix:\n";
adjoint(A, adj);
display(adj);

cout << "\nInverse Of The Matrix:";
if (inverse(A, inv)) { cout << "\n";
display(inv); }

return 0;
}
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