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Analyzing perturbation of vectors

  1. Feb 24, 2013 #1
    1. The problem statement, all variables and given/known data

    We have [itex]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 [/itex]

    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. jcsd
  3. Feb 24, 2013 #2


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