This problem concerns the equation Ax = b , where                                                 and α > 0. (a) For what values of α is this matrix ill-conditioned? Make sure to identify what norm...

This problem concerns the equation
Ax
=
b, where

and α > 0.

(a) For what values of α is this matrix ill-conditioned? Make sure to identify what norm you are using.

(b) Suppose the residual
r
is small (but nonzero). For what values of α, if any, will the error
e
=
x
−
x
_c
be large? Note
x
is the exact solution and
x
_c
is the computed solution.

(c) Suppose the error
e
is small (but nonzero). For what values of α, if any, will the residual be large?