Use row reduction to show that:
[1 1 1]
[a b c] = (b-a)(c-a)(c-b)
[a^2 b^2 c^2]
The Attempt at a Solution
So I multiplied -a by row 1 and added it to row 2. I then multiplied -a^2 by row 1 and added it to row 3, which gave me:
[1 1 1]
[0 b-a c-a]
[0 b^2-a^2 c^2-a^2]
Now, at this point, I was already quite confused, as I don't know how I did that (I was following the book). Where did the -a and -a^2 come from? Thin air? How was I to know to multiply a (as opposed to b or c)?
Anyway, after that, I did cofactor expansion and expanded the b^2-a^2 and the c^2-a^2 to get (b-a)(b+a) and (c-a)(c+a). This is pretty much where I got up to. I think I'm close, but I don't know what to do next. Suggestions? Advice? Hmm?