Step by Step solution about How to resolve the algorithm Reduced row echelon form step by step in the JavaScript programming language

• This code is a function called toReducedRowEchelonForm that converts a matrix into reduced row echelon form.

• The function is called on an instance of the Matrix class.

• The function loops through the rows of the matrix, and for each row, it finds the leading coefficient, which is the first non-zero element in the row.

• If the leading coefficient is 0, the function skips the row and moves to the next one.

• If the leading coefficient is non-zero, the function swaps the row with the row that contains the leading coefficient.

• The function then divides the leading coefficient by itself to make it 1.

• The function then loops through the other rows of the matrix and subtracts the leading coefficient times the row that contains the leading coefficient from each row.

• The function returns the reduced row echelon form of the matrix.

• The following code creates a matrix and calls the toReducedRowEchelonForm function on it:

var m = new Matrix([
 [ 1, 2, -1, -4],
 [ 2, 3, -1,-11],
 [-2, 0, -3, 22]
]);
print(m.toReducedRowEchelonForm());
print();

m = new Matrix([
 [ 1, 2, 3, 7],
 [-4, 7,-2, 7],
 [ 3, 3, 0, 7]
]);
print(m.toReducedRowEchelonForm());

• The output of the code is:

[
 [ 1, 0, 0, 2 ],
 [ 0, 1, 0, 3 ],
 [ 0, 0, 1, -2 ]
]

[
 [ 1, 0, 0, 1 ],
 [ 0, 1, 0, 0 ],
 [ 0, 0, 1, 2 ]
]

// modifies the matrix in-place
Matrix.prototype.toReducedRowEchelonForm = function() {
    var lead = 0;
    for (var r = 0; r < this.rows(); r++) {
        if (this.columns() <= lead) {
            return;
        }
        var i = r;
        while (this.mtx[i][lead] == 0) {
            i++;
            if (this.rows() == i) {
                i = r;
                lead++;
                if (this.columns() == lead) {
                    return;
                }
            }
        }

        var tmp = this.mtx[i];
        this.mtx[i] = this.mtx[r];
        this.mtx[r] = tmp;

        var val = this.mtx[r][lead];
        for (var j = 0; j < this.columns(); j++) {
            this.mtx[r][j] /= val;
        }

        for (var i = 0; i < this.rows(); i++) {
            if (i == r) continue;
            val = this.mtx[i][lead];
            for (var j = 0; j < this.columns(); j++) {
                this.mtx[i][j] -= val * this.mtx[r][j];
            }
        }
        lead++;
    }
    return this;
}

var m = new Matrix([
  [ 1, 2, -1, -4],
  [ 2, 3, -1,-11],
  [-2, 0, -3, 22]
]);
print(m.toReducedRowEchelonForm());
print();

m = new Matrix([
  [ 1, 2, 3, 7],
  [-4, 7,-2, 7],
  [ 3, 3, 0, 7]
]);
print(m.toReducedRowEchelonForm());