Gaussian Elimation with Partial Pivoting Algorithm by hand

[medinaj2160]

Homework Statement

The Gaussian Elimination with Partial Pivoting algorithm when applied to the following matrix

A[-3 0 4; 5 2 -6; 0 0 1]

Will construct matrices P, L, and U

1- What are the defining properties of the matrices P, L and U?

2- What relation do P, L, U and A always satisfy?

3- Given that

L=[1 0 0, -3/5 1 0; 0 0 1]

What are P and U?

Homework Equations

PA=LU

The Attempt at a Solution

How do I do this by hand?
There is rref command on the Ti89, the is lu(A), A\b, inv(A)*b on matlab...

Anyways I know how to get the answer by doing this http://www.youtube.com/watch?v=euIXYdyjlqo" but I don't know how to construct the matrices that he wants, this is not homework is a review for a test on Monday.

I know
P= is the permutation matrix= it switches rows
L= lower triangular matrix
U= upper triangular matrix.

So I need, to this by hand. Can someone send link or help me on how to do this step by step?

Thanks

 

[medinaj2160]

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