Compute the LU factorization of the matrix
A=
[2 1 1]
[4 1 0]
[-2 2 1]
and solve A[ = ][8 11 3
using back substitution.
Let A=
[1 1 1]
[1 1 2]
[1 2 5]
Find a permutation matrix so that PA has an LU factoriza-
tion. Compute L and U.
this is should be an easy question, but it's been so long since i ve done matrix, so any help will be appreaciated..
Partial pivoting is about exchanging rows so that you are always pivoting on the entry in the column with largest absolute value. It's to try to prevent what's referred to as swamping.
Since all the entries in the first column are the same, you don't need to exchange any rows.
It's a good idea to put the multipliers in parenthesis so that you can keep track of them when you exchange rows.
In this problem it's not about swamping, but rather the fact that you can't pivot on a zero. So exchange rows 2 and 3. The permuatation matrix for such a exchange is
then