## Why is this better?

- Solving triangular matrices is easy: just use forward substitution for (1), backsubstitution for (2).

## Problem is, how to decompose

*A*into*L*and*U*?- Expand matrix multiplication
*LU*to get*n*2 equations for*n*2 +*n*unknowns (elements of*L*and*U*plus*n*extras because diagonal elements counted twice). - Get an extra
*n*equations by choosing*Lii*= 1 (*i*= 1,*n*). - Then use
__Crout's algorithm__for finding solution to these*n*2 +*n*equations "trivially" (NRiC 2.3).

- Expand matrix multiplication