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Explain an entangled state vector and how it behaves with respect to: (a) inner products, and...
We equip the vector space R2 with a (non-standard) inner product (with respect to the standard basis E- {(1,0)", (0, 17) is ), whose metric Let L: R2 → R2 be the reflection operator with respect to the x-axis, defined by 21 21 Compute the adjoint operator Lt. Is L self-adjoint?
We equip the vector space R2 with a (non-standard) inner product (with respect to the standard basis E- {(1,0)", (0, 17) is ), whose metric
Let L: R2 →...
a. Suppose that we have the state l) 2-1/2 (1010)1100)). How many (and which) particles are b. Suppose instead that we have the state l) 212(l000) |111). How many (and which) c. Suppose you measure the first particle from part (b) in the |0), |1) basis. What are the possible entangled? Explain why. particles are entangled? Explain why outcomes and their probabilities? On average, how many particles are entangled after the เงื่ measurement?
a. Suppose that we have the state...
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉 ∈ R for x, y ∈ V . (a) (3points) Let λ∈R with λ>0. Show that 〈x,y〉′ = λ〈x,y〉, for x,y ∈ V, (b) (2 points) Let T : V → V be a linear operator, such that 〈T(x),T(y)〉 = 〈x,y〉, for all x,y ∈ V. Show that T is one-to-one. (c) (2 points) Recall that the norm of a vector x ∈ V...
Explain how mustard gas behaves as a DNA adduct and how it affects DNA?
Problem 6. Let V be a vector space (a) Let (--) : V x V --> R be an inner product. Prove that (-, -) is a bilinear form on V. (b) Let B = (1, ... ,T,) be a basis of V. Prove that there exists a unique inner product on V making Borthonormal. (c) Let (V) be the set of all inner products on V. By part (a), J(V) C B(V). Is J(V) a vector subspace of B(V)?...
Explain the significance of the pKa with respect to the protonation state and charge of an ionizable group, and calculate the isoelectric point (pI) of a polyprotic weak acid. Please give an example
How to solve all of this linear
Algebra
8. (24 points total) LetV be the vector space{P2, +, *}with standard function addition and scalar multiplication Define an Inner product: <p | q>= p(0)q[O) + p(1)q(1)+ p(2)q(2). Let B = {x,x,1} a. Explain why this inner product satisfies the positive property b. Explain how you know that B forms a basis c. State the conclusions of Cauchy-Schwartz and the Triangle inequalities in terms of this inner product d. Use Gram-Schmidt and...
(g) Explain how to get the demand curve for labor. (h) Explain how to determine output in an economy with a labor market. (i) Explain how to find the stationary state in a Solow model. (j) Explain how the economy behaves out of the stationary state in a Solow model.
15 points) You are given a carbohydrate to analyze. It behaves as a reducing sugar with a Tollen's test. When you exhaustively methylate it with alkaline CH3l and then hydrolyze with strong acid, you get the following in an equal molar ratio (1:1); 2,3,4,6-tetra-o-methylgalactose 2,3,6-tri-O-methylglucose You try reacting it with different glycosidases, and get the following results: a-galactosidase: No reaction B-galactosidase: produces galactose and glucose (1:1) as products a-glucosidase: No reaction B-glucosidase: No reaction . (2 point) Based upon these...
QUESTION 2 Consider the vector space R3 (2.1) Show that (12) ((a, b, c), (x, v, z))-at +by +(b+ c)(y + z) is an inner product on R3 (2.2) Apply the Gram-Schmıdt process to the following subset of R3 (12) to find an orthogonal basis wth respect to the inner product defilned in question 2.1 for the span of this subset (2.3) Fınd all vectors (a, b, c) E R3 whuch are orthogonal to (1,0, 1) wnth respect to the...