User:Djmvfb/cs228

Open Condition Systems

Example 1

Consider the following two equations:

${\begin{matrix}f(x):\ &4x-3y&=&2\\g(x):\ &x+y&=&10\end{matrix}}$

What would happen when the coefficient on one variable was changed slightly? For instance:

${\begin{matrix}f(x):\ &4x-3y&=&2\\g_{1}(x):\ &(1.001)x+y&=&10\end{matrix}}$

There is only a very slight change (which isn't even noticeable on the graphs). Whereas the intersection of $g(x)\$ and $f(x)\$ was at $(4.5714,\ 5.4286)$, the slightly altered $g_{1}(x)\$ brings the intersection to $(4.5695,\ 5.4259)$. The distance between the two dots is only 0.003302 units, which is generously negligible.