Solutions of Test 1
MA407H
1. The set cfw_2, 4, 6, 8 forms a group under multiplication modulo 10.
(a) (10 points) Construct a Cayley table for this group.
(b) (10 points) What is the identity element in this group?
(c) (10 points) Is this group cyclic? J
Solutions of Test 2 MA407H
Directions: On the test one cheat sheet is allowed to be used:
it is a single letter size page, both sides hand written by you.
No other aid (books, notes, calculators or any other kind) will be
allowed. The total number of poin
Solutions of Test 3 MA407H
1. Prove that S = cfw_m/n Q : m, n Z, gcd(m, n) = 1, n odd is a
subring of Q. Is S an ideal of Q?
Solution: Let a/b and c/d in S . Then a/b c/d = (ad bc)/bd is in S since
bd is odd, and all its divisors are odd. Similarly, (a/b)
Practice Test 3 MA407H
Directions: On the test one cheat sheet is allowed to be used:
it is a single letter size page, both sides hand written by you.
No other aid (books, notes, calculators or any other kind) will be
allowed.
1. Let R =
a b
c d
| a, b, c
Solutions of Practice Test 2 MA407H
Directions: On the test one cheat sheet is allowed to be used:
it is a single letter size page, both sides hand written by you.
No other aid (books, notes, calculators or any other kind) will be
allowed.
1. Prove that t
Practice Test 2 MA407H
Directions: On the test one cheat sheet is allowed to be used:
it is a single letter size page, both sides hand written by you.
No other aid (books, notes, calculators or any other kind) will be
allowed.
1. Prove that the only subgr
Solutions of Practice Test 1
MA407H
Directions: On the test one cheat sheet" is allowed to be used: it is a single letter size page,
both sides hand written by you. No other aid (books, notes, calculators or any other kind) will
be allowed. You will have
Practice Test 1
MA407H
Directions: On the test one cheat sheet" is allowed to be used: it is a single letter size
page, both sides hand written by you. No other aid (books, notes, calculators or any other
kind) will be allowed. You will have 50 minutes. M