__Condition number__cond(*A*) = (max*Wi*)/(min*Wi*).- If cond(
*A*) = ,*A*is__singular__. - If cond(
*A*) very large (106, 1012),*A*is__ill-conditioned__.

- If cond(
## Consider

*A***x**=**b**. If*A*is singular, there is some subspace of**x**(the__nullspace__) such that*A***x**= 0.## The

__nullity__is the dimension of the nullspace.## The subspace of

**b**such that*A***x**=**b**is the__range__.## The

__rank__of*A*is the dimension of the range.