Have you ever tried to teach math to anyone who is not good at math? In my youth I once tutored a woman who was poor, but motivated enough to pay $40/session. A major obstacle was teaching her how to calculate (a^b)^c and getting her to reliably notice that minus times minus equals plus. Despite my attempts at creative physical demonstrations of the notion of a balanced scale, I couldn't get her to really understand the notion of doing the same things to both sides of a mathematical equation. I don't think she would ever understand what was going on in matrix calculus, period, barring "teaching methods" that involve neural reprogramming or gain of additional hardware.