Having lived with and helped rehabilitate a stroke victim the first step isn't to give them new ways to 'speak'.
Motivation to do things the old way needs to be provided first, step 1 is to identify just how much cognitive ability remains - simple things like a picture of an apple with text on it - Is this an Apple? This tests a number of 'skills' that we take for granted but these could be damaged in some way i.e the ability to read, to recognise objects - clearly Matt seems to be able to recognise family so that's good, he can respond to audio stimuli so that too is good.
Only when you know how much of the 'old Matt' remains can you hope to help and it is too early to know that. The white board idea that's not bad, simple games like 'O's and 'X's - build on the no yes responses - keep the stimulation going.
I'm afraid those around Matt will need to have boat loads of patience, partly because they remember him as he was and will have as much trouble adjusting as Matt does in recovering, Matt will probably be more frustrated than they are, be unable to show it and hence will react in unexpected ways - depends how much of the old Matt is trapped inside trying to reach out but unable to do so.
Probably the best thing that forum members could do right now is to get behind his family, 3 weeks in terms of a brain injury is nothing. Sounds to me as though Matt will need a lot of support going forward, his family and their supporters need to be given the support to keep them going so that they can keep Matt going.
I really don't want to come over as a killjoy but I've lived with a close relative that suffered brain damage through a stroke, I lived with the ups / the downs whilst trying to do the normal day to day things and live my life at the same time. What helped us were those that said - hey we will cut your grass, no let me go for the groceries, look after the children and even provided an ear or just the company to permit the venting of some frustration etc etc.
As for people that feel a need to help Matt and are close enough to do so should support his family, let them take care of Matt - and the Doctors of course.