Math 3130 Midterm: Due Wednesday October 22 in Class Remember to show your work! Summary: Math 3130 Midterm: Due Wednesday October 22 in Class Remember to show your work! Directions This is a take home, open notes test. There are eight problems on the test. You must answer carefully and completely any five of the problems. You answer must be your own; you are free to discuss problems with other students but must write up your own answers. Excessive similarity of answers will be noted and dealt with appropriately. Problem 1 Find all possible cycle types in S5 and say how many permutations there are with each cycle type. Problem 2 Compute GCD(54, 45) = 54x + 45y using the Euclidean algorithm and solving for x and y by back substitution through the Euclidean algorithm. Problem 3 Let A be a group with two elements and so that A consists of all possible products in any order of and . If and satisfy the following relations: 3 = 3 = ()2 = e Prove the following identities hold in A. (i) = 2 2 , (ii) = 2 Collections: Mathematics