Determine whether or not W is a subspace of R3 where
W consists of all vectors (a,b,c) in R3 such that
1. a =3b
2. a <= b <= c
3. ab=0
4. a+b+c=0
5. b=a2
6. a=2b=3c
1.Determine whether S spans V . Justify your answers.
V = C ^0 [−1, 1] (the vector space of continuous functions on
[−1, 1]) and S = {1, t, t2 , t3 , . . . }.
2.Let S be a set in a vector space V and v any vector. Prove
that span(S) = span(S ∪ {v}) if and only if v ∈ span(S).
Let (V, ||·||) be a normed space, and W a
dNormV,||·|| -closed vector subspace of
V.
(a) Prove that a function |||·||| : V /W → R≥0 can be
consistently defined by ∀v ∈ V : |||v + W||| df= inf({||v + w|| :
R≥0 | w ∈ W}).
(b) Prove that |||·||| is a norm on V /W.
(c) Prove that if (V, ||·||) is a Banach space, then so is (V
/W, |||·|||)
If V (dimension k-1) is a subspace of W (dimension K),
and V has an orthonormal basis {v1,v2.....vk-1}. Work out a
orthonormal basis of W in terms of that of V and the orthogonal
complement of V in W.
Provide detailed reasoning.
Determine whether the following statements are true or false , and
justify your answer
1- Given that accounting information is a public good , we
have to have mandatory accounting regulation.
2- It is better to lobby the accounting standard - setter
indirectly rather than directly.
3- A change in reported income is an economic consequence of a
change in an accounting standard's requirements
PLEASE JUSTIFY EVEN IF YES
Determine whether each of the following statements is true or
false. Justify your answer for any that you think are false.
a) The margin of error for a 95% confidence interval for the
population proportion p increases as the sample size increases.
b) The margin of error for a confidence interval for the
population proportion p, based on a specified sample size n,
increases as the confidence level decreases
. c) The margin of error for a 95% confidence interval...
Determine whether it is true of false and justify your
answer.
Every nonempty bounded set S of real numbers has a
supremum and infimum, but those might not be elements of the
set.