Finding the matrix row echelon form using Gaussian elimination

Here’s an example Java code that demonstrates how to find the row echelon form of a matrix using Gaussian elimination:

public class RowEchelonForm {

    public static void main(String[] args) {

        double[][] matrix = {

                {2, 1, -1, 8},

                {-3, -1, 2, -11},

                {-2, 1, 2, -3}

        };

        int rows = matrix.length;

        int cols = matrix[0].length;

        System.out.println("Original Matrix:");

        printMatrix(matrix);

        for (int i = 0; i < rows; i++) {

            // Find the pivot element

            int pivotRow = i;

            double pivot = matrix[pivotRow][i];

            for (int j = i + 1; j < rows; j++) {

                if (Math.abs(matrix[j][i]) > Math.abs(pivot)) {

                    pivotRow = j;

                    pivot = matrix[j][i];

                }

            }

            // Swap rows if necessary

            if (pivotRow != i) {

                double[] temp = matrix[i];

                matrix[i] = matrix[pivotRow];

                matrix[pivotRow] = temp;

            }

            // Perform row operations to eliminate lower triangular elements

            for (int j = i + 1; j < rows; j++) {

                double ratio = matrix[j][i] / matrix[i][i];

                for (int k = i; k < cols; k++) {

                    matrix[j][k] -= ratio * matrix[i][k];

                }

            }

        }

        System.out.println("\nRow Echelon Form:");

        printMatrix(matrix);

    }

    private static void printMatrix(double[][] matrix) {

        int rows = matrix.length;

        int cols = matrix[0].length;

        for (int i = 0; i < rows; i++) {

            for (int j = 0; j < cols; j++) {

                System.out.printf("%.2f\t", matrix[i][j]);

            }

            System.out.println();

        }

    }

}

This code takes a 2D array representing a matrix as input. It uses the Gaussian elimination algorithm to transform the matrix into row echelon form. The `printMatrix` method is used to display the original matrix and the row echelon form.