Question

Prove that σ(a2) = σ(a)2 = {λ2 : λ ∈ σ(a)}

Answer #1

Please prove (a1+a2+……+an)^2/n ≤ (a1)^2 + (a2)^2 +……+
(an)^2.

Please do both:
a. Suppose that A ∈ Mn is non-singular. Prove that if λ ∈ σ(A),
then λ −1 ∈ σ(A−1 ).
b. If λ ∈ σ(U) and U ∈ Mn is unitary, show that |λ| = 1.

Let Wn be a wheel with n vertices. Prove that P(Wn, λ) =
λ(λ-2)^n + (-1)^n(λ-2).

What is the wavelength, λ, of a resulting wave of two
co-propagating waves with λ1, λ2, that have the same frequency and
the same amplitude?

prove that iΛ : Λ → Λ is a function which represents
the set Λ as an indexed family with index set Λ.

Prove that if x~Pois(λ). then E(x)=λ

Let n∈N, and let a1,a2,...an∈R. Prove that
|a1+a2+...+an|<or=|a1|+|a2|+...+|an|

Suppose thatA∼N(μ= 3,σ= 5),B∼N(μ= 2,σ= 4), andC∼Exp(λ= 1/6)
areindependent RVs. Find the distribution (shape, center, spread)
of the following RV expressions and state whether the distribution
is exactly or approximately equal to your claim.
1.D=A+B
2.E= 3A−2B
3.F=A1+A2+···+A14, whereA1,...,A14are independent values
fromA.
4.G=C1+C2+···+C47, whereC1,...,C47are independent values
fromC.

Question 3. Let a1,...,an ∈R. Prove that
(a1 + a2 + ... + an)2
/n ≤ (a1)2 + (a2)2 +
... + (an)2.
Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for
all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T).
Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above
and T is bounded below. Let U = {t−s|t ∈ T, s...

(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪
A2 ∪ ... ∪ An is countable. (Hint: Induction.)
(6) Let F be the set of all functions from R to R. Show that |F|
> 2 ℵ0 . (Hint: Find an injective function from P(R) to F.)
(7) Let X = {1, 2, 3, 4}, Y = {5, 6, 7, 8}, T = {∅, {1}, {4},
{1, 4}, {1, 2, 3, 4}}, and S =...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 15 minutes ago

asked 17 minutes ago

asked 29 minutes ago

asked 37 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago