Letting suppose that ∇ = 0 yields the equation Av = b. It was shown that for this to happen A must be symmetric. The purpose of this exercise is to show that the properties of B are more flexible. To...

Letting

suppose that ∇
= 0 yields the equation
Av
=
b. It was shown that for this to happen
A
must be symmetric. The purpose of this exercise is to show that the properties of
B
are more flexible. To do this, assume that

(a) Show that
A
is positive definite.

(b) Find a nonsymmetric
B.

(c) Find a symmetric but not positive definite
B.

(d) Is it possible for
B
to be diagonal?

(e) Is it possible for
B
to be non-invertible?