Abstract Algebra Answers

Solve the equation 1+sinθ =cos2θ
, 0 ≤2π≤θ

suppose A,B are n- square skew-symmetric matrices.prove that AB is symmetric if and only if A and B commute.

3 people are standing one behind the other. There are 2 red caps and 3 green caps, place on their heads. They can only see what the guy in front is wearing. The last guy is asked the color of his cap. he says "i don't know". The guy in the middle is also asked the same question. He also says "i don't know". But the first guy answers correctly. What color was he wearing?

if 6 divided by 3 is 2 then just multiply from back see just reverse 2 times 3 is 6

Letters processed: 12,151
Total postage: 4489.32

X= letters w/postage of .36
Y=letters w/postage of .384

Problem some of these letters were stamped with a postage rate of .36 and some with a postage rate of .384, figure out how many were processed at each rate.

The mean clotting time of blood is 7.47 seconds with a standard deviation of 3.6 seconds. What is the probability that an individual's blood-clotting time will be less than 7 seconds or greater than 8 seconds?

Please do not work it out using calculus.

B ⊆ R is a minimal right ideal of R iff B = eR where e ∈ R has rank 1.

Show that A ⊆ R is a minimal left ideal of R iff A = Re where e ∈ R has rank 1.

For any r ∈ R of rank m (i.e. dimk rV = m), show that there exist r1, . . . , rm ∈ Rr of rank 1 such that r = r1 + • • • + rm.