One of my lecture notes showing a 3x3 matrix, let's name this matrix Y. I am confused about the result Y^-1. I am trying to find some study material for relating to Y^-1, and I couldn't find any useful information(actually I still don't know how professor got his answer) I guess the material I studied wasn't right. Could anyone can provide the searching key words for learning this related subject?
Sure, Y^-1 is the inverse of Y. When you multiply the two matricies together you get the Identity matrix Code ( (Unknown Language)): Y*Y^-1 = I = [ 1 0 0 ; 0 1 0 ; 0 0 1] Many software packages like Matlab, Scilab, and R will give you the inverse of a 3 x 3 matrix in the twinkling of an eye. I've heard tell that inverting one by hand is possible by using minors and cofactors but I haven't done it recently. Inverting a 4 x 4 or larger is definitely not -- you'll excuse the expression -- a hand job.
http://www.mathcentre.ac.uk/resources/leaflets/firstaidkits/5_5.pdf Shows you a common method.. I have had to do inversions of 4X4 matrices on math exams, it sucks Steve
PB, I recall the manual approach was quite laborious. You are right to suggest numerical packages like Matlab, which is expensive, so look at one of the matrix-based (free) alternatives: http://forum.allaboutcircuits.com/blog.php?b=65 Dave
Don't overlook the fact that Microsoft EXCEL has a matrix function that can be used to perform matrix manipulation. hgmjr