## Numerical methods also have problems when:

- Equations are degenerate "within round-off error".
- Accumulated round-off errors swamp solution (magnitude of
*a*'s and*x*'s varies wildly).

## For

*n,m*< 50, single precision usually OK.## For

*n,m*< 200, double precision usually OK.## For 200 <

*n,m*< few thousand, solutions possible only for sparse systems (lots of*a*'s zero).