Problem Set

(See attached file for full problem description) a) Determine the irreducibility of x20-11 over Q(set of rationals), and use it to prove or disprove that the ideal is a maximal ideal of Q[x]. b) Construct an integral domain R and an element a in R such that a is irreducible but not prime in R. c) Suppose that R is ...continues

Series convergence

Prove that the series Sigma (k = 0 to inf) k!/k^k converges

Series Convergence of a Recurrence Relation

Prove that the series given by the recurrence relation a_n+1 = SQRT(3*a_n), where a_1 = 4, converges, and find the limit of convergence.

Multiplicative groups

(See attached file for full problem description) --- a) Recall the following definitions of the multiplicative groups GLn(k) and SLn(k) over a field k: GLn(k)={invertible n x n matrices over k} SLn(k)={A in GLn(k) such that the determinant of A=1} Prove th ...continues

Find the orbit and stabilizer of the given matrix under multiplication by matrices of the specified type.

Find the orbit and stabilizer of the 2 X 2 matrix M under the action of multiplication of M by the matrices in GL_2(R), where the top row of M is (1 0) and the bottom row is (0 2). [That is, m_11 = 1, m_12 = 0, m_21 = 0, and m_22 = 2.] See attached file for full problem description.

Eigenvalues, eigenfunctions and modified Green's function.

5.6. (a) Find the eigenvalues and eigenfunctions of —u”=λu, —1 ...continues

Frobenius Norm of a Matrix

Please see the attached file for the fully formatted problems.

This is a Financial Management Problem

1) You have been hired as a financial consultant to Jane Corporation, a large, publicly traded firm. The company is looking at setting up a manufacturing plant overseas. The project will be for five years. The company bought some land three years ago for $4.2 million in anticipation of using it as a possible plant site, but the ...continues

Exponential Functions

One of the archeologists you interviewed for your article is graphing asymptotes to illustrate the data generated through carbon dating the half-life of fossil specimens. Help him with his work by solving these problems: Explain and contrast the types of asymptotes considered for rational functions. Browse through some news ...continues

College Math

I have been asked to explain and contract the types of asymptotes considered for rational functions. I have located the following but truly am having a difficulty understanding it. Thus, I have no idea what the below means unfortunately and I am therefore truly at a loss. Hopefully a better understanding of this will assist ...continues