Question

In: Advanced Math

1.Determine whether S spans V . Justify your answers. V = C ^0 [−1, 1] (the...

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).

Solutions

Expert Solution

Colby Messinger answered 1 year ago
Next > < Previous

Related Solutions

Determine whether or not W is a subspace of V. Justify your answer. W = {p(x)...
Determine whether or not W is a subspace of V. Justify your answer. W = {p(x) ∈ P(R)|p(1) = −p(−1)}, V = P(R)
Determine whether the polynomial is reducible or irreducible in the given polynomial ring. Justify your answers....
Determine whether the polynomial is reducible or irreducible in the given polynomial ring. Justify your answers. (c) x^4 + 1 in Z5[x] (e) 2x^3 − 5x^2 + 6x − 2 in Z[x] (f) x^4 + 4x^3 + 6x^2 + 2x + 1 in Z[x]. Hint: Substitute x − 1 for x.
Determine whether it is true of false and justify your answer. Every nonempty bounded set S...
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.
Indicate whether each statement is True or False. Briefly justify your answers ( Please answer C...
Indicate whether each statement is True or False. Briefly justify your answers ( Please answer C and E both ) (c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0) is a vector space under the usual matrix operations of addition and scalar multiplication. ( e) If x⃗1 and x⃗2 are in the null space of a square matrix A, then any linear combination of x⃗1 and x⃗2 is also in the null...
Determine whether each of the following statements is TRUE or FALSE. Justify all the answers in...
Determine whether each of the following statements is TRUE or FALSE. Justify all the answers in few sentences. 1. In the Ricardian model with 2 goods (Wine and Cheese) and 2 countries (Home and Foreign) and (except otherwise noted) identical preferences between countries: (a) If both countries have the same number of workers and Home has absolute advantages in both goods then Home must have a higher wage. (b) The Home country is never made worse off by productivity growth...
Determine whether each of the following statements is TRUE or FALSE. Justify all the answers in...
Determine whether each of the following statements is TRUE or FALSE. Justify all the answers in few sentences. 1. In the Ricardian model with 2 goods (Wine and Cheese) and 2 countries (Home and Foreign) and (except otherwise noted) identical preferences between countries: (a) If both countries have the same number of workers and Home has absolute advantages in both goods then Home must have a higher wage. (b) The Home country is never made worse off by productivity growth...
Answer whether or note the following statements are true, false or uncertain. Justify your answers. 1....
Answer whether or note the following statements are true, false or uncertain. Justify your answers. 1. The Lucas critique argues that the simple Keynesian multiplier model cannot be used to evaluate the potential impact of policy because the model’s assumption of a representative agent is too simple to capture the real world. 2. Ricardian Equivalence implies that the government’s fiscal policy does not matter.
Determine whether each system is LTI, causal and/or stable and with or without memory. Justify answers....
Determine whether each system is LTI, causal and/or stable and with or without memory. Justify answers. a) y[n + 1] + 4y[n] = 3x[n + 1] - x[n] b) y[n] = nx[2n]
Determine whether each system is LTI, causal and/or stable and with or without memory. Justify answers....
Determine whether each system is LTI, causal and/or stable and with or without memory. Justify answers. a) y(t) =sen(x(t)) b) y(t) = dx/dt + x(t)
Determine whether the following statements are true or false , and justify your answer 1- Given...
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
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT