12. Which of the following can be eigenfunctions of the operator d/dx? Is an eigenfunction of d/dx Is NOT an eigenfuction of d/dx sin(ax) sin(ax) + cos(bx) eax еax + ebx eax2 Clear selection

Q: [a11(t) a12(t) 1) Let A(T) = be differentiable. %3D Show that: d (det (A(t)) = det a 12 (t)] la21(t)…

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Q: Q1) Express in matrix notation: x' = (cos 2t) x y' = x – (sin 2t)y +1 z' = 1- x + 3y

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Q: 2. Show that for any x, the matrix A = A² = I. [cos(2x) sin(2x) [sin(2x) − cos(2x)] - satisfies the…

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Q: Find the fourier transform of the following. functions by making use of Jordan's Lemma. a) 1 (x² +…

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Q: Find a linear differential operator that annihilates the given function 1+6x-4x3

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Q: sin x COS X [ COS X - sin x

A: Answer and explanation is given below..

Q: dz (b) Determine the by using the Chain rule with the following information: ds z = cos (rªy^) – sin…

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Q: Let {Cn} be the complex Fourier coefficients of f, 27-periodic, i.e. coefficients wrt the…

A: (1) Given that cn be the fourier coefficient of f. Let fn be the fourier coefficient of…

Q: 7. For R, let A = Ag = cos sin sin 0 cos sin 0 and B Be= 86). cos cos sin (a) Show that B has an…

A: The rotation matrix in 2D is given.

Q: nd a sequence of elementary matrices whose product is the standard matrix for counterclockwise [cos…

A: The standard matrix for counterclockwise rotation through angle  about the origin is

Q: T1(t) x2(t) a Suppose x'(t) = Ax(t) where A = , а, b, с, d € R and z(t) — Use the d 0, definition of…

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Q: Let the eigenvalues and eigenvectors of matrix A4x4 be 21 = -5, v1 = d2 = 6, v2 = d34 = -3 + 2i,…

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Q: . Prove that the matrix A = Cos 0 sin 0 - sin 0 cos - has no real eigenvalues for 0 < 0 < T.

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Q: 5 - Calculate the Fourier transform of 100 – 5t 0 <t< 20 f(t) = otherwise

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Q: 92 Solve the PE Eup (Initial value 79₁ 1 O O 01 1 problem) its inco)

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Q: Eigenvector of when a = 5 A. 1 B.[] BG CH DH

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Q: Show that the matrix is invertible and find its inverse. 9] A-1 = A = sin 8 [₁ cos Ꮎ -cos 0 sin 0

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Q: If A is a real 2x2 matrix and has eigenvalues A, μ that are purely imaginary, then solution curves…

A: Let A be 2×2 real matrix. Let eigen vector corresponding purely imaginary complex numbers λ, μ be…

Q: Verify that u(x, y) = x² − 6x²y²+y¹ is harmonic everywhere and determine its harmonic conjugate.

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Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: 0 0 1 cos(0) -sin(@)) sin(0) cos(0) 1 1 (a) (c) 0 1 0 (d) -1 | 1 0 0

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Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: | ^ | ≈ 1 for every eigenvalue à;

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: Which of the following is True about the Fourier transform of the signal x(t) = u(t) — u(−t)? - X(w)…

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Q: 2. Show that the wavefunction (eigenfunction) of a state |a) can be expressed in position basis as…

A: The wavefunction (or eigenfunction) of a state |α⟩ can be expressed in the position basis as ⟨x|α⟩.…

Q: If my matrix contributes eigenvalue A = 3+ 4i with corresponding eigenvector v = [i, 1]. What are…

A: We will find out the required solution.

Q: 4. Form the inner product to show that the operator du Lu rE (0, 1) %3D da? Bru = u(0) Bau = u'(1)…

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Q: Exercise 1 Find the fourier series for the function. a) f(x) = { * if 0 <r< T 27 – if n <a < 27 and…

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Q: A.) Use a change of variables to generate expressions for 6 (t-t) and 6(w-wo) B. ) Use the…

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Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ

Q: 6) Find Fourier transform of: 8 1) e-n(v²+y) (x − y)e-lx-v\dy 88 f 2) nye dy -πy²

A: According to our guidelines,i can solve only one please reroute the remaining question.