Let $T: \Bbb R^3 \rightarrow \Bbb R^3$ be the linear transformation given by reflecting across the plane $S=\{x:-x_1+x_2+x_3=0\}$ (...) 

Then, $S=\gen[(1,1,0),(1,0,1)]\$

But how can I get the matrix $R_v$ such that reflects across $S$? 

Thanks!


Question: How can you (anybody) find out the IP address of a single computer inside college
Answer: I suppose that our situation is the following: you have detected some undesirable network traffic and you are looking for the perpetrator, so as to, more or less metaphorically, convey to him the inherent unwisdom of his villainous behaviour. The source address of the offending IP packets points to a college; the college uses Network Address Translation so that outgoing traffic from all their students is seen, from the outside, as coming from a single IP address.

(Or, possibly, you are the wannabe evildoer and you want to know what the Long Arm of the Law could do to trace you back. It does not change the technical situation.)

Strictly speaking, the college acts as a kind of anonymizer, since it blocks the actual (internal) IP information. So you should ask the college. They may have detailed logs on network activity, which may help pinpoint the uncivilized individual; for instance, the DHCP logs within the college network could give some information on who had their computer up and running at the time of the indelicacy. There are various sources of such information, which depend a lot on the structure of the internal college network.

Be sure to bring all the information you have on your side; network traces obtained with a network monitor application (like Wireshark or the aptly named Network Monitor) are a must. Also, bring all logs, especially Web server logs, because Web browsers tend to produce a lot of information which can be quite specific to the specific computer which sends the requests (see this page for details).