ut.jl

function swap_col(A, i, j)
    col_i = A[:,i]
    col_j = A[:,j]

    A[:,i] = col_j
    A[:,j] = col_i
end

function swap_row(A, i, j)
    row_i = A[i,:]
    row_j = A[j,:]

    A[i,:] = row_j
    A[j,:] = row_i
end

function move_entry(A, i, j, m, n)
    swap_row(A, i, m)
    swap_col(A, j, n)
end

function add_row(A, i, j, k)
    A[i,:] += k*A[j,:]
end

function strike_col(A, j)
    for i = (j + 1):size(A,1)
        println(-(A[i,j]*(1/A[j,j])))
        add_row(A, i, j, -(A[i,j]*(1/A[j,j])))
    end
end

function choose_non_zero(A, j)
    for i = j:size(A,2)
        for k = j:size(A,1)
            if A[k,i] != 0
                return (k,i)
            end
        end
    end

    return (0,0)
end

function make_ut(A)
    for j = 1:(size(A,1) - 1)
        (alpha, beta) = choose_non_zero(A,j)

        if alpha == 0
            return A
        end

        move_entry(A, alpha, beta, j, j)
        strike_col(A, j)
    end

    return A
end

println(make_ut([1.0 3.0 2.0; 3.0 2.0 4.0; 5.0 -6.0 3.2]))

Transforms a matrix A into an upper triangular matrix, using only row operations of type 1 and 3.