VBA to insert this first monday of the week date function/value

I am trying to replace my worksheet function which generates a date for the first monday of the weekday when given a date. I have managed to create a VBA code that works to insert this function in to cells. It is very ugly and slow and may make some of you sick to your stomach. I was hoping someone could provide a more reasonable way for trying to accomplish this task.

'Insert Week Begin Formula into Column L
    
    rw = 2
    
    Do While Cells(rw, 1) <> ""
        
        Cells(rw, 12) = "=IF($A2<>"""",DATE(YEAR($A2),MONTH($A2),DAY($A2)-WEEKDAY($A2,3)),"""")"
        
    rw = rw + 1
    Loop
    
'Copy the row references down for the Week Begin Formula
    Dim LastRow As Long
    LastRow = Cells(Rows.Count, "L").End(xlUp).Row

    Range("L2").Select
    Selection.AutoFill Destination:=Range("L2:L" & LastRow)

That code works well when I paste it into Column L and copy it down. However, how would I rewrite that code to have the vba populate the cell for me (either with the formula itself or the value)?

A-K are part of an exported .xls file and I will need column L to create itself.

I tried incorporating the code from post #2 into my code from post #1 and got:

'Insert Week Begin Formula into Column L
    
    rw = 2
    
    Do While Cells(rw, 1) <> ""
        
        Cells(rw, 12) = "=A2+(8-MOD(WEEKDAY(A2),7))-6"
        
    rw = rw + 1
    Loop
    
'Copy the row references down for the Week Begin Formula
    Dim LastRow As Long
    LastRow = Cells(Rows.Count, "L").End(xlUp).Row

    Range("L2").Select
    Selection.AutoFill Destination:=Range("L2:L" & LastRow)

The result is that it copies the same formula placed in cell A2 all the way down. It stops at the correct row but the row references are not changing. What does the code look like to have these cell references change as they are copied down??

Here is your code, revised to calculate Monday dates based on the date
listed in column A, and put them in column L. This code defines the week
as Sunday through Saturday, but you can use the alternate Saturday through Friday
code commented out, if needed.

Your loop was not coded correctly, as it was just duplicating the same thing for each row.
Since you chose to use AutoFill, I removed the unnecessary looping code.

Sub Test_1()
'Insert Week Begin Formula into Column L
Dim LastRow As Long, rw As Long
    
    LastRow = Cells(Rows.Count, "A").End(xlUp).Row

    'Cells(2, 12).Formula = "=A2+(8-MOD(WEEKDAY(A2),7))-6"   'uses week of Saturday thru Friday
    Cells(2, 12).Formula = "=A2+(7-WEEKDAY(A2)-5)"           'uses week of Sunday thru Saturday
    
    'Copy the row references down for the Week Begin Formula
    Range("L2").Select
    Selection.AutoFill Destination:=Range("L2:L" & LastRow)
    
    'change formulas to values
    For rw = 2 To LastRow
        Cells(rw, 12).Value = Cells(rw, 12).Value
    Next
    
End Sub