# Using QR decomposition to find a nontrivial solution to Ax=0

1. Apr 5, 2009

### Random Variable

1. The problem statement, all variables and given/known data

Supposedly the process to solve Ax=0 is to solve Transpose(R).Ry=z (where z is a random vector) and then x=y/(norm-2 of y).

2. Relevant equations

3. The attempt at a solution

Ay=b for some random vector b

Transpose(A).Ay= Transpose(A).b

Transpose(QR).QRy=Transpose(A).b

Transpose(R).Transpose(Q).QRy = z where z is Transpose(A).b

Transpose(R).Ry=z since Q is orthogonal

Then x (the solution to the homogeneous system) is y/(norm-2 y)? But why?

Last edited: Apr 5, 2009