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After spending several days with a naive approach to linear algebra I can tell you: it doesn’t work. Will use a third party implementation because my implementation is way too slow. My very short and elegant implementation (only 500 lines) works well for smal problems but miseralby fails with anything of substantial size. The failure means that the soluion is obtained after a noticeable period of time (1-2 seconds) which is not acceptable for a pleasant interactive experience.
If you wonder why I would need such a beast in IDA, ask yourself how it can be used. There is a chance to win a contest:

http://www.datarescue.com/ubb/ultimatebb.php?/topic/4/375.html