# Thread: How to find lower tri matrix

1. ## How to find lower tri matrix

I have to factor the matrix into the LU decomposition with the LU factorization algorithm with lii = 1 for all i.

A =
[2 -1 1]
[3 3 9]
[3 3 5]

U =
[2 -1 1]
[0 9/2 15/2]
[0 0 -4]

L =
[1 0 0]
[1.5 1 0]
[1.5 1 1]

I know how to get U from just row reducing but I don't get how L is found.

2. Originally Posted by JackRyder
I know how to get U from just row reducing but I don't get how L is found.
The algorithm is that (1) you should reduce A to rref from U without row interchanges, keeping track of the multipliers you used to introduce leading 1's. And multipliers you used to get zeros below the leading 1's. (2) In each position along the main diagonal of L, place the reciprocal of the multiplier that introduced the leading 1 in that position in U. (3) In each position below the main diagonal of L, place the negative of the multiplier used to introduce the zero in that position in U. Now you can form the decomposition A=LU, have you tried following this algorithm?

3. I see, so that's how you get it. I couldn't understand the pseudo-code used to describe the LU Factor Algorithm.

Thanks.