Analyzing perturbation of vectors

[autobot.d]

Homework Statement

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

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.

 

[LCKurtz]

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