> My textbook isn't really clear in this topic. Is > there a fixed set of elementary operations for > finding an equivalent matrix, or is it done purely by > trial/error and logic?
From: Doctor Nisith Bairagi Uttarpara, West bengal, India Sub: MATRIX INVERSION Date:Marcch 12, 2013 .............................. Dear Mathematican,
I also pose a problem on matrix: Associated with the famous Fibonacci sequence, namely: 1,1,2,3,5,8,13,21,..., (where every third number is the sum of the second and first number),the two roots of the quadratic equation x^2 - x - 1 = 0, show that their difference = 1. That is, x - 1/x = 1. Then, can any body tell me, what will be the matrix [A]so that the difference of [A] and its inverse [inv A]will result in a unit matrix [I]? That is,if [A] - [inv A] = [I], [A] = ? In the same line, please tell me,a second one : if [A] + [inv A] = 6[I], [A] = ?
Please send the answer in this column, and also to my email address: <firstname.lastname@example.org>
Thanks from: Doctor Nisith Bairagi [Retired Professor of Structural Engineering, IIT-Bombay, India.]