Adjusting a do loop for matrix algebra?

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I am trying to write a program in Maple to create a lower-triangular matrix. My professor provided a do loop in class that creates an upper-triangular matrix, but I don't even understand how that works, so I can't change the code to make it create a lower-triangular matrix instead.

Given the matrix A:

I can use the code:

for j to 4 do

for i to 4 do

if i > j then

c := -A[i, j]/A[j, j];

for k to 4 do

A[i, k] := c*A[j, k]+A[i, k]

end do

end if

end do

end do;

... which results in the matrix,

How can I adjust this code to make it do lower-triangular instead? I don't even understand the upper-triangular code. I understand Gaussian elimination, but I don't understand how this code works because of the nested loops.

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