This problem considers the question, why not use UL instead of LU? You can assume that A is a 2 × 2 matrix. (a) Find a Doolittle version of the factorization A = UL , where L is a unit lower...

This problem considers the question, why not use UL instead of LU? You can assume that
A
is a 2 × 2 matrix.

(a) Find a Doolittle version of the factorization
A
=
UL, where
L
is a unit lower triangular matrix and
U
is upper triangular. You can assume pivoting is not necessary.

(b) Describe the resulting algorithm for solving
Ax
=
b.

(c) Is there any connection between the Doolittle factorization of
A

^T

and the one you found in part (a)?

(d) Aside from an alphabetic advantage, is there any reason to prefer LU over UL?