Using the inner product on 〈p, q〉 = ∫(0 to1) p(x)q(x)dx on P2, write v as the...

Using the inner product on 〈p, q〉 = ∫(0 to1) p(x)q(x)dx on P2, write v as the sum of a vector in U and a

vector in U⊥, where v=x^2, U =span{x+1,9x−5}.

Expert Solution

Colby Messinger answered 2 years ago

Let V = {P(x) ∈ P10(R) : P'(−4) = 0 and P''(2) = 0}. If V=...

Let V = {P(x) ∈ P10(R) : P'(−4) = 0 and P''(2) = 0}. If V= M3×n(R), ﬁnd n.

Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕...

Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕ q) is equivalent to p ^ q. Please show your work and name all the logical equivalence laws for each step. ( v = or, ~ = not, ⊕ = XOR) Thank you

Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p...

Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p) ⊕ (p v ~q) is equivalent to p v q. v = or, ~ = not, ⊕ = exclusive or (XOR). Please show the steps with the name of the law beside each step, thanks so much!

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1)...

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x, x2} for P2. (a) Find the matrix A for T with respect to the basis B. (b) Find the eigenvalues of A, and a basis for R 3 consisting of eigenvectors of A. (c) Find a basis for P2 consisting of eigenvectors for T.

Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such...

Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such that the differential equation has solutions sinx and 1+cosx. Finally, find a homogeneous third order differential equation with constant coefficients where sinx and 1+cosx are solutions.

Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V...

Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V (x) = U for x > L Write down the Schrödingerequation and solutions (wavesolutions) on general form for the three V(x).

Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y)))...

Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y))) P2: (∃x)(∀y)(P(x) ∧ ((Q(y) ∧ R(x, y)) ⇒ S(x, y))) C: ∼ (∀x)(∀y)((P(x) ⇒∼ T(x, y)) ∨ (Q(y) ⇒ R(x, y)))

Suppose V is a ﬁnite dimensional inner product space. Prove that every orthogonal operator on V...

Suppose V is a ﬁnite dimensional inner product space. Prove that every orthogonal operator on V , i.e., <T(u),T(v)> = <u,v>, ∀u,v ∈ V , is an isomorphism.

Consider the “step” potential: V(x) = 0 if x ≤ 0 = V0 if...

Consider the “step” potential: V(x) = 0 if x ≤ 0 = V0 if x ≥ 0 (a) Calculate the reflection coefficient for the case E < V0 , and (b) for the case E > V0.

We have potential of V (x) = ( 0, 0 ≤ x ≤ a. ∞, elsewhere....

We have potential of V (x) = ( 0, 0 ≤ x ≤ a. ∞, elsewhere. a) Find the ground state energy and the first and second excited states, if an electron is enclosed in this potential of size a = 0.100 nm. b) Find the ground state energy and the first and second excited states, if a 1 g metal sphere is enclosed in this potential of size a = 10.0 cm. c) Are the quantum effects important for...

Question