On the contrary, that is precisely the "L" in the "LU" form.

Here's how I would get L: 'zero' out the area above the diagonal using row operations andkeeping trackof the row operations.

We can change to

by "subtract 3 times the first row from the second" and "subtract 1 times the first row from the third"

We can change that matrix to

in "upper triangular" form by "add the second row to the third row".

Now, do theoppositeoperations, in theoppositeorder, to the identity matrix.

That is, first "subtractthe second row from the third row" to get

and then "add1 times the first row to the third" and "add3 times the first row to the second" to get

Now you can check that

or LU= A.