rankMatrix.cpp

// C++ program to find rank of a matrix
#include <bits/stdc++.h>
using namespace std;
#define R 3
#define C 3

/* function for exchanging two rows of
a matrix */
void swap(int mat[R][C], int row1, int row2,
		int col)
{
	for (int i = 0; i < col; i++)
	{
		int temp = mat[row1][i];
		mat[row1][i] = mat[row2][i];
		mat[row2][i] = temp;
	}
}

// Function to display a matrix
void display(int mat[R][C], int row, int col);

/* function for finding rank of matrix */
int rankOfMatrix(int mat[R][C])
{
	int rank = C;

	for (int row = 0; row < rank; row++)
	{
		// Before we visit current row 'row', we make
		// sure that mat[row][0],....mat[row][row-1]
		// are 0.

		// Diagonal element is not zero
		if (mat[row][row])
		{
		for (int col = 0; col < R; col++)
		{
			if (col != row)
			{
				// This makes all entries of current
				// column as 0 except entry 'mat[row][row]'
				double mult = (double)mat[col][row] /
									mat[row][row];
				for (int i = 0; i < rank; i++)
				mat[col][i] -= mult * mat[row][i];
			}
		}
		}

		
		else
		{
			bool reduce = true;

			/* Find the non-zero element in current
				column */
			for (int i = row + 1; i < R; i++)
			{
				// Swap the row with non-zero element
				// with this row.
				if (mat[i][row])
				{
					swap(mat, row, i, rank);
					reduce = false;
					break ;
				}
			}

			// If we did not find any row with non-zero
			// element in current columnm, then all
			// values in this column are 0.
			if (reduce)
			{
				// Reduce number of columns
				rank--;

				// Copy the last column here
				for (int i = 0; i < R; i ++)
					mat[i][row] = mat[i][rank];
			}

			// Process this row again
			row--;
		}

	// Uncomment these lines to see intermediate results
	// display(mat, R, C);
	// printf("\n");
	}
	return rank;
}

/* function for displaying the matrix */
void display(int mat[R][C], int row, int col)
{
	for (int i = 0; i < row; i++)
	{
		for (int j = 0; j < col; j++)
			printf(" %d", mat[i][j]);
		printf("\n");
	}
}

// Driver program to test above functions
int main()
{
int mat[][3] = {{10, 20, 10},
				{-20, -30, 10},
				{30, 50, 0}};
	printf("Rank of the matrix is : %d",
		rankOfMatrix(mat));
	return 0;
}