Let T be a linear operator on a finite-dimensional vector space V, and let x be a nonzero vector in V. Prove the following results. (a) The vector x has a unique T-annihilator. (b) The T-annihilator of X divides any polynomial git) for which 9(T) = T(). (c) If p(t) is the T-annihilator of x and W is the T-cyclic subspace generated by x, then />(
Math 340 Lecture – Introduction to Ordinary Differential Equations – March 28 , 2016 th What We Covered: 1. Worksheet 9 a. Highlights i. We went over a lot of the problems in class but the rest of the work sheet was homework so I won’t be giving the answers on here 2. However, the general way to solve the problems on the work sheet and for the upcoming quiz is: a. Assuming you have the equation = where A is a square matrix i. First, find the eigenvalue = (−1) det − = 0 ii. From there we can find the eigenvector by ( − ) b. We can then format the final solution exponentially:
