Let x = (x1, . . . , xn)T be an eigenvector of A belonging to . Show that if |xi| = _x_, then (a) _n j=1 ai j x j = xi (b) |aii| _n j=1 j _=i |ai j | (Gerschgorins theorem)

Math 1314 Lesson 1: Prerequisites 1. Simplifying Algebraic Expressions 1 2 1 Example 1: Simplify 15x (2x 3 x ) 3x (x x ) 5 . 3 2. Identifying Polynomials To begin with, let’s review the definition of a polynomial function. A polynomial is the...