LU factorization to solve Ax = b

[Quincy]

Homework Statement

A is a 4 x 5 matrix equal to
[1 4 -1 5 3
3 7 -2 9 6
-2 -3 6 -4 1
1 6 9 8 2]

and b =
[5
40
15
12]

(b is 4 x 1)

Find the LU factorization and use it to solve Ax = b

Homework Equations

The Attempt at a Solution

I set Ly = b, and solve for y, then I set Ux = y, and when I row-reduce the Augmented [U y] matrix, I always get a 4 x 1 matrix, but x is supposed to be 5 x 1, what am I doing wrong??

 

[lkh1986]

LU decomposition
Applicable to: square matrix A

http://en.wikipedia.org/wiki/Matrix_decomposition

In your case, A is a 4x5 matrix.

Or there's actually a way to find he LU decomposition for a non-square matrix?

 

[Quincy]

Or there's actually a way to find he LU decomposition for a non-square matrix?

There was an example of it in the book; it only found L and U for the 4x5 matrix though, it didn't show how to solve Ax = b.

 

[hotvette]

There was an example of it in the book; it only found L and U for the 4x5 matrix though, it didn't show how to solve Ax = b.

That's because there are potentially an infinite number of solutions. The system you have is what's called an 'underdetermined' system that has fewer equations than unknowns. There is a 'minimum norm' solution that can be found via other factorization techniques (QR or SVD), but not LU (at least I don't think so).