Finals hit like a whiplash... you know it's going to arrive before it hits, but the wait is almost an eternity. And when it finally hits, it's gone before you can finish blinking ... and you don't even feel the effects till the next morning...
I studied my ass off. I'm certain I got A's in all finals ... not necessarily classes ... except math, because that damned final question was so tricksy ...
(XT is short for "the transpose matrix of matrix X" and Rn can be thought of as a coordinate space of real numbers where n is the number of axes.(Here we assume the plural for axis, not axe. :-D )
If A is an n*n matrix in Rn, and AT = - A, what is the determinant of A if n = 3 ? If n = 4 ?
Dammit, I looked at this question from every angle and could only see ZERO for both answers.
I looked it up in another book and found that such a matrix is called a skew matrix and IF n is odd, then, indeed, the determinant is zero. But it says nothing about the determinant when n is even ! I'll get to the bottom of this shortly !
Update: Jacobi's Theorem explains it all.
It would've been nice to know that one before the test. >:-(
I don't know why my brain skipped out on that when thinking about it with diagonals and what not. Grrr.