# Analyzing perturbation of vectors

1. Feb 24, 2013

### autobot.d

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

We have $A \in R^{mxm} \text{ and } b \in R^{m} \text{ and } b \neq 0 \text{. Show that } Ax = b \text{ and } A(x+ \delta x) = b+ \delta b$

3. The attempt at a solution

I did the first part just by the definition of A being non singular. The second part is tripping me up though. Not sure how to tackle it. I looked at the backwards stability but it just confused me more. Any help would be most appreciated.

Last edited: Feb 24, 2013
2. Feb 24, 2013

### LCKurtz

If $Ax=b$ doesn't $A(x+\delta x)= b +\delta b$ just follow by linearity?