MATH 342 Study Guide - Midterm Guide: Coding Theory, Coset, Group Theory
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The exam is 150 minutes long and worth a total of 100 points. No books, notes or calculators may be used. Show all of your work and justify your answers carefully. You will be graded on the clarity of your exposition as well as the correctness of your answers. Math 342 section 101 december 2010 page 2 of 14. Inverse elements: calculate the inverse of the following elements in z/18z. (a) [11]18 (b) [7]18 (c) [15]18. Math 342 section 101 december 2010 page 3 of 14. Group theory: the following set of 2 2 matrices. 0 1(cid:19) m3 = (cid:18) 1 m1 = (cid:18)1 0 m5 = (cid:18)0 1. 1 with matrix multiplication forms a group, g. (a) (2 points) list the elements of its subgroup, k, generated by the element (cid:18)1. 0 (b) (8 points) compute the left cosets of k. Math 342 section 101 december 2010 page 4 of 14.
