1. Prove these properties of Householder matrices 2. Prove that if is chosen to be parallel to vector where but 2 2 then u Let where is a constant, and note that Compute and apply the...

1.

Prove these properties of Householder matrices

2.

Prove that if

is chosen to be parallel to vector

where

but

<sub>2

2</sub>

then

_u


Let

where

is a constant, and note that

Compute

and apply the relation

_u

Show that

and apply Theorem 17.3, part