I have a matrix A = $$ \begin{pmatrix} 12 & 17 & 29 \\ 0 & 0 & 0 \\ 5 & -7 & -2 & \\ \end{pmatrix} $$
I am trying to figure out the condition number $c(I+A)$ with respect to $\left\lvert \right\rvert$ $\left\lvert \right\rvert$$_\infty$. Im not super sure how to approach this at all.Im really trying to figure out this so I can attack a problem I keep encountering in
Let $v$ and $\delta v$ be such that $(I+A)v=[1,1,1]^T$ and $((0.999)I+A)(v+\delta v)=[1,0.99,1^T]$. Compute $\left\lvert \right\rvert$${\delta v} $$\left\lvert \right\rvert$$_\infty$ / $\left\lvert \right\rvert$$ v $$\left\lvert \right\rvert$$_\infty$ and compute the upper bound given by the "condition on equations" theorem to make a comparison...
Again, I'm clueless on how to attack both of these. I've already computed the QR-decomposition of A and solved the least squares problem along with (However, I think I may have gotten that wrong as well) if that information would help.