1. For what values of is ill-conditioned What happens as 2. Prove that for any orthogonal matrix for any matrix . 3. There is an equivalent definition of The condition number of a nonsingular...

1. For what values of

is

ill-conditioned
What happens as

2. Prove that for any orthogonal matrix


for any

matrix
.

3. There is an equivalent definition of

The condition number

of a nonsingular matrix

is

where

_n
is the set of singular

matrices.

If

is ill-conditioned, what does this say about the relative distance of

from the subset of

singular matrices

Ifis a well-conditioned matrix, answer the question of part