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.