Huh? It's right there: second column, fourth box down. You could quibble that it isn't "one of the techniques", but the effect of that is to invalidate your original complaint that all the chart tells you to do is to apply known techniques.
OK, I looked at the arrows. (1) What's your point? (2) Is there any actual reason why you haven't said already what it is, rather than all this "Look at the flowchart" / "Look at the arrows" nonsense?
There is an arrow from "Do known techniques apply?", labelled "No". It leads to "Try to find a new technique". There's an arrow back from there to "Do known techniques apply?". Obviously, if you succeeded in finding a new technique applicable to the problem, the set of "known techniques" has expanded and you then follow the "Yes" arrow from "Do known techniques apply?".
Is it your opinion that there is something wrong with this? If so, what?
(If you respond with another passive-aggressive "Look at X" reply, I shall ignore it unless looking at X immediately convinces me that you've been right all along and I've been missing something.)
(1) When I see the phrase "known techniques" in the context of math it generally refers to techniques known in the field. Novel techniques are not "known" in this sense. The different, literal, trivial interpretation of "known" makes the word superfluous. That was the motivation for my first comment. In both cases (your point of view being the second) my comment is true; by this flowchart a technique must be known to be applied. The only way I could see someone disagreeing is if they're confused about what "known" means.
(2) It seemed obvious, and moreover too trivial a point to merit more than just pointing it out. I apologize if I've caused any offense.
* To clarify, I don't consider "find a new technique" to be a technique, which is why I said to look at the arrows.
Please don't dismiss the "literal, trivial interpretation". If you read the explanations that came with the flowchart, they try to make it very clear that "known" means "known to you".
Also consider the context. This was a handout to students in a first linear algebra class, that was meant to help them learn to do basic proofs on their homework problems. Nobody expected them to be engaged in original research. Any useful technique they needed to "discover" was very likely to be well-known to lots of people, including me.
Finally it is not clear to me why you think that the word "known" is superfluous. There is a world of difference between the stage where you are running through the techniques you know, trying to find one that fits, and the stage where you're engaged in expanding your list of available techniques. I was trying to get at that difference.
