Q1:3 Evaluate the following commutators acting on the Hilbert space of L² (R) functions and conclude whether they commute or not (i) d x, dx (ii) |x, dx?

Q: evaluate the Pirst and second deriugive of f) = 327+5csin 3x• %3D at x= 11 , 2.5 &3.7

A: To evaluate the first and second derivatives of f(x)

Q: For which value of x is A = x= 4 1 -4 4 0 0 1 NOT invertible? -3 r

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Q: 2х1 + 3х, — хз — 2 Зх1 — 2х2 + хз — —1 = -1 — 5х1 — 4х2 + 2xз — 3

A: Given that  The system of equations  To find the solution of system of equations by using cramers…

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) =…

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Q: Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a…

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Q: Consider the interpolating polynomial for f(x) = x³ based on th points (0,0), (1,1) and (2,8). Find…

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Q: Q1: Sketch the signals A. x(t) x(-1/2) A CL x(2(1+2)) x(−1+1) Ates Ades 0 2 B. 2 x(t) 0 1 x (3t),…

A: Given data:- Part A=   Part B

Q: 1. Answer all parts. (a) Consider the operators A and B. Show that (i) (ii) [A, B]=-[A, B] [Am, A"]=…

A: Operators :A and B

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: 1. Let Q(v2) = {a+b/2| a, b E Q}. Prove that Q(/2) = Q[x]/(x² – 2).

A: We have to show that isomorphism means there is function ϕ such that we have to show that it is an…

Q: Compute 5f – 7g, given that f(r) - and g(z) - e. -1) "(z-1) Se

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Q: 1) Evaluate g = Af, where A and f are given below: (a) (b) (c) (d) A SQRT d³ dr³ + x³ dx 8² 8² +…

A: The step-by-step answer is given below please check.Explanation:Step 1:a) Step 2:b) Step 3:4)…

Q: Determine whether the following set of polynomials is linearly independent (1 – t)?, t – 2t2 + t³,…

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Q: Let f.g.h:A - A be any bijective functions. Then (g oh on-

A: (g∘h∘f)-1=f-1∘h-1∘g-1 composition of function is associative…

Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

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Q: 2х1 + 3x2 — хҙ — 2 Зx1 — 2х2 + Xз — —1 -1 %3D -5x1 4x2 + 2x3 = 3

A: Consider the provided equations, 2x1+3x2-x3=23x1-2x2+x3=-1-5x1-4x2+2x3=3 Solve the above equation by…

Q: 5d rd-2a 2b a D. 5e-h If det d Lg h i 1, compute det e If - 2c %3D C 5f-

A: To compute determinant of the given matrix.

Q: Gue Functions fandg, FindCa) Cf g) C&) and its dlomiain, and b) (g oF (x) and its. O F(x)--6xtq,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let X be a pre-Hilbert space then [(x, y)|

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Q: Let x,y,z  be (non-zero) vectors and suppose w=10x−5y+3z If z=y−2x mark the statements below that…

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Q: Q 4. (a) Prove or disprove that for any real numbers x and y, [x + y] = [x] + Lyl (b) Find the…

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Q: Let|a| = 32, the number of right cosets of (a²) in is:

A: Given          |a| = 32 Then, <a> = { a , a2 , a3 ,  .  .  .  , a32 = e } ,  where e =…

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A: vector q is not in the span of vectors.  p1,p2and p3. complete explanation is given…

Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

A: Solution:

Q: dx In x +1+ Vx² + 2x| + C Vx2 + 2x

A: