Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero.

Problem 1: Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero. Problem 2: Prove that no pair of the following groups of order 8, I8; I4 x I2; I2 x I2; D8; Q, are isomorphic.

Algebraic Structures

Problem #1 Prove that Aut(V)= (S3)and that Aut(S3)= S3. Problem #2 If H and K are normal subgroups of a group G with HK = G. Prove that G/(H n K) = (G/H) x (G/K).

Algebraic Structures : Quaternions and Dihedral Groups

The problem I need help with is in this attached sheet (# 264).

Algebraic Structure

I would love to have a usual word format answer with detailed proofs. The problems are 6 in total, the numbers are: from attached page #1: #2.82; 2.86; 2.87, from attached page #2: # 2.97; 2.98; 2.99. Thanks in advance. The student.

Tree diagram

The Knicks won the first game against the Lakers in a basketball playoff. If the first team to win four games is the winner, construct a tree diagram for this playoff. Hint: Some of the branches in the tree diagram will end sooner than the other , as one of the teams would have one four games.

Probability: make sample space and find probabilities

Use a tree diagram. Use a diagram to list the sample space showing possible arrangements of heads and tails when four coins are tossed . Then use the sample space to find the probability that: 1. at most two coins come up heads 2. at least two coins come up heads 3. no more than three coins come up tails.

Percent

What is 5% of 5000.00

A couple of I think quick questions . . .

Hi! I'm using old tests to study for an abstract algebra exam and of course the old exams do not come with solutions. This means that I need help. I tend to struggle with proofs because I forget some steps or I am not as rigorous as I should be. Thus I need to see actual complete rigorous proofs so that I can make sure that I re ...continues

Ring Ideal

Could you please help me with the attached question 33 parts a, c, and d Let R be the ring of all continuous functions...

Proofs : Groups, Subgroups, Tower Law and Isomorphisms

1.) Suppose [G:H] is finite. Show tat there is a normal subgroup K of G with K, a subgroup of H, such that [G:K] is finite. 2.) Suppose H is a subgroup of S_n but H is not a subgroup of A_n. Show that [H:A_n intersect H]=2. 3.) Prove that if H,K are normal subgroups of G and HK=G, then G/(H inters ...continues