ah ha! Thank you. Dot with b and re-arrange to give an expression for
x.b, substitute that into the original equation, rearrange a bit more
- seemed to work, but why? I'd got as far as x = (c - a x.b) / alpha
before, and thought i didn't have enough equations to be able to say
anything about x.b , but it seems i can get more information out by
operating on the whole of the original equation. Instead I'd tried all
sorts of generally applicable substitutions into the original
equation, only to fill a couple of pages with scribble.
Working through the subsequent exercises, it seems that operating on
the whole equation to learn more about it is often useful. I wonder
why the text didn't introduce this heuristic. Maybe it's considered
too obvious, but nothing in my intuition from scalar algebra led me to
It feels like there is a lot of flexibility in GA, but so far it feels
like you need magic to navigate that. Does the magic feel more
systematic after a while?