MATH 3001 Study Guide - Midterm Guide: Identity Matrix, Gaussian Elimination, Linear Combination
Document Summary
Please do not think that the info on this page is something you should have memorized (except for the rst listthat"s important). Rather, these facts may be helpful to use in problems, but are fairly straightforward to prove (so understand them, but don"t go overboard in memorizing them). The following facts regarding the inverse of a matrix apply so long as a and b are invertible: (cid:0)a 1(cid:1) 1. = a: (ka) 1 = k 1a 1 for k 6= 0, (cid:0)at(cid:1) 1. = (cid:0)a 1(cid:1)t: (ab) 1 = a 1b 1, det(cid:0)a 1(cid:1) = det(a) The following facts regarding the transpose of a matrix apply for any matrices a, b and scalar c: (cid:0)at(cid:1)t. = a: (a + b)t = at + bt, (ab)t = bt at, (ca)t = cat, det(cid:0)at(cid:1) = det(a, if a is a square matrix, then its eigenvalues are equal to the eigenvalues of its transpose.
