Questions
Find the characteristics and the minimal polynomial of the following matrices over R, then deduce the their corresponding Jordan Canonical Form J.

Find the characteristics and the minimal polynomial of the following matrices over \( \mathbb{R} \), then deduce the their corresponding Jordan Canonical Form J.

A=\( \begin{pmatrix}1&-1&-1\\ 0&0&-1\\ 0&1&2\end{pmatrix}\: \)

In: Advanced Math

Find all eigenvalues and their corresponding eigenspaces of the following matrix.

Find all eigenvalues and their corresponding eigenspaces of the following matrix. B=\( \begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \)

In: Advanced Math

Find all eigenvalues and their corresponding eigenspaces of the following matrix.

Find all eigenvalues and their corresponding eigenspaces of the following matrix. A.\( \begin{pmatrix}3&0\\ 1&2\end{pmatrix} \)

In: Advanced Math

show that for some ring R, the equality a2−b2=(a−b)(a+b) holds ∀a,b∈R if and only if R is commutative.

 show that for some ring R, the equality a^2−b^2=(a−b)(a+b) holds ∀a,b∈R if and only if R is commutative.

In: Advanced Math

Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.

Show that the relation 'a R b if and only if a−b is an even integer defined on the Z of integers is an equivalence relation.

In: Advanced Math

In a finite cyclic group, each subgroup has size dividing the size of the group. Conversely, given a positive divisor of the size of the group, there is a subgroup of that size

Prove that in a finite cyclic group, each subgroup has size dividing the size of the group. Conversely, given a positive divisor of the size of the group, there is a subgroup of that size.

In: Advanced Math

Measure Theory

Let f be measurable and B a Borel set. Then f-1[B] is a measurable set. [Hint: The class of sets for which f-1[E] is measurable is a σ-algebra.

In: Advanced Math

Let G be finite with |G| > 1. If Aut(G) acts transitively on G − {e} then G ∼= (Z/(p))n for some prime p.

Let G be finite with |G| > 1. If Aut(G) acts transitively on G − {e} then G ∼= (Z/(p))n for some prime p.

In: Advanced Math

How do you calculate the probability of compound events?

How do you calculate the probability of compound events?

In: Advanced Math

Find and Simplify where ................................

Find f(a+h) - f(a) / h where f(x) = 6x - 9

In: Advanced Math

What is the number of group homomorphisms from z12 to z13?

What is the number of group homomorphisms from z12 to z13?

In: Advanced Math

What is the vertex of y = 2x² + 6 x + 4 ?

What is the vertex of  

y=2x²+6x+4  ? Give details explaination

In: Advanced Math

concave function

What x values is the function concave down if  f(x)=15x⅔+5x ?

In: Advanced Math

Number Theory

Given integers a, b, c,

g.c.d.(a, b, c) = 1 if and only if g.c.d.(a, b) = 1 and g.c.d.(a, c) = 1

In: Advanced Math

syllw subgroup

The number of involutions in G is |G|/4, and every right coset of a Sylow 2-subgroup S of G not contained in NG(S) contains exactly one involution.

In: Advanced Math