Some MATLAB functions to create matrices representing steps in Gaussian Elimination

function interchangeRows = interchangeRows(i, j, n, m)
A = eye(n,m);
A(i,i) = A(j,j) = 0;
A(i,j) = A(j,i) = 1;
interchangeRows = A;

function multiplyRowbyScalar = multiplyRowbyScalar(j, alpha, n, m)
A = eye(n,m);
A(j, j) = alpha;
multiplyRowbyScalar = A;

function multiplyRowIbyScalarAddRowJ = multiplyRowIbyScalarAddRowJ(i, j, alpha, n, m)
A = eye(n, m);
A(j, i) = alpha;
multiplyRowIbyScalarAddRowJ = A;