LU Factorization - Linear Algebra LU-factorization

My solution:

Am I on the right path? Or am I completely off?

You seem to be using a modification of the Doolitle algorithm, but some steps or data are missing, because the last matrix multiplication does not give the correct result: e.g. in the right bottom corner your matrices give $3*(-2) + (-4)*2 + 1*(-1) = -15$, and not $1$.
While was checking the calculations, a correct answer was given by Kundor. Just in case you are interested, here is what I get using SMath Studio:
 
