Abstract Algebra Answers

Linear mathematics Question

The set M2,2 of 2 × 2 matrices, with real entries, is a vector space.
The set of antisymmetric matrices A = { 0 a }
−a 0
where a belongs to R is a subset of M2,2.
Prove that A is a subspace of M2,2.

Part 2

Select any two integers between -12 and +12 which will become solutions to a system of two equations.
Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. Use the example on page 426 of Mathematics in Our World as a guide.
Respond to at least two of your classmates’ postings. Do you agree or disagree that their examples model functions? Follow their 5 steps. Do their calculations follow the correct rules of algebra?

The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs

a. None fuses

b. Not more than 2 fuse

c. More than 2 fuse

On a rectangular hyperbola, if one point is (2, 3) and y varies inversely to x, find y when x is 6.

A coin was tossed 10 times and the outcomes noted as H,T,H,H,T,T,T,T,H,T where H is Head and T is Tail. Find the estimated probability of a tail.

33 1/3%+p=100% p=

need to figure this problem:

if 3x2 - 2x +7 = 0, then (x - 1/3)2 =

Let G be a group and H be a subgroup of G. Define the normalizer of H in G by N(H)={g in G| gHg^(-1)=H}. Prove N(G) is a subgroup of G.

Give an example of a group G and two elements a,b in G such that "the order" |ab| does not equal "the order" |a||b|.

determine whether the given relation is an equivalence relation on the set:
(a)nRm in R if n>=y