Abstract Algebra Answers

Consider the set of matrices
G = a = 1 0
0 1;b = 0 1
1 0;c = 1 1
0 1;d = 1 0
1 1;e = 1 1
1 0; f = 0 1
1 1
with coefficients in Z2.
a) Make the Cayley table and check that this set forms a group with respect to matrix
multiplication. (You can assume that matrix multiplication is associative.)
b) Find the orders of all the elements in G.
c) Show that the group is isomorphic to S3 by giving an isomorphism f : G -> S3.

Solve the following system of equations, state the method that you would use, and show all work to solve:

5x - 3y = - 4
3x - y = - 4

x + 5y = 12
5x + 25y = 12

x + y = - 2
- 3x - 3y = 6

Two private airplanes travel toward each other from cities that are 780 km apart at speeds of 190 km/h and 200 km/h. They left at the same time. In how many hours will they meet?

The owner of The Daily Grind coffee shop mixes French roast coffee worth $9.00 per pound with Kenyan coffee worth $7.50 per pound in order to get a 10 pound mixture worth $8.40 per pound. How much of each type of coffee was used?

The two most common names for streets in the United States are Second Street and Main Street, with 15,684 streets bearing one of these names. There are 260 more streets named Second Street than Main Street. (Source: 2006 Tele Atlas digital map data) How many streets bear each name?

a cabinet, 4 chairs and 2 tables cost $825. The cabinet costs 3 times as much as a chair. The table costs $120 more than a chair. What is the cost of the cabinet.

find the value of x
4x+5a=2x-15a

Simplify the following Boolean function:
F = A’C + A’B + AB’C + BC, using K-map?

How many Boolean functions on two independent Boolean variables a and b are dependent on either a or b or both?

Use mathematical induction to prove the statement is true for all positive integers n.

The integer n3 + 2n is divisible by 3 for every positive integer n.

Help me please