Below is my script, which basically creates a zero matrix of 12x8 filled with 0. Then I want to fill it in, one by one. So lets say column 2 row 0 needs to be 5. How do I do that? The example below shows how I did it and the wrong (for my needs) output:

list_MatrixRow = []
list_Matrix = [] #Not to be confused by what the book calls, optimal alignment score matrixint_NumbOfColumns = 12
int_NumbOfRows = 8for i in range (0, int_NumbOfColumns): # Puts Zeros across the first Rowlist_AlignMatrixRow.append(0)
for i in range (0, int_NumbOfRows):list_AlignMatrix.append(list_AlignMatrixRow) 
#add the list in another list to make matrix of Zeros
#-------------------THE ACTUAL PROBLEMATIC PART; ABOVE IS FINE(It Works)------------list_AlignMatrix[2][0] = 5 
# This is what logically makes sense but here is the output 
# which happens but I don't want (there should be all 0s and 
# only one 5 on the cell [2][0]):[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Each row points to the same sublist. This is the result of appending the same sublist repeatedly. So when you modify one row, you end up modifying the others.

I would do this:

ncols = 12
nrows = 8
matrix = [[0] * ncols for i in range(nrows)]
matrix[2][0] = 5 

matrix contains:

[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

An aside about coding style: It is poor form in Python to include the type of the object in its name. I have chosen to rename int_NumbOfColumns as ncols. If you need something more descriptive use something like column_count. Generally, mixedCase names are to be avoided, while CamelCase is generally used for class names. See PEP 8 -- Style Guide for Python Code for more.

Edit: Since you mentioned that you are new to Python, here's a little more explanation.

This is a list comprehension:

matrix = [[0] * ncols for i in range(nrows)]

It can also be written as a regular for-loop:

matrix = []
for i in range(nrows):matrix.append([0] * ncols)