1. To show that the transform x - Ax = (x1- 2.x2 + x3,3x1+ x2,2x2 – x3), = (r1,#2, 13) E R³ is linear from R³ into R³ and find Az for z = (-2, 1, 1) ;

Q: 4. (a) Prove that H, { f(x) [Hn-1{f(x)} + Hn+1{f(x)}] and hence find T. 2n S (x – a) Hn ,a > 0, k >…

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Q: Which of the following is the Laplace transform of the solution to the initial value problem x" –…

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Q: - What function f(t) has Laplace transform: 2s +3 3s +6 s²-4s +13 + 2 s + 3s

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

Q: Give the Laplace transform of 0<x and x <5 5 <x and x <7 -3 f(x) = -2 -s - e +4 e-5- e7+0e-7. FYs) =…

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Q: 1 The Laplace transform of the solution of the following Cauchy problem ´y" (t) − y'(t) + 3y(t) =…

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Q: 1 Find the inverse transform: F(s) s2+4s+4

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Q: 1.25 In comparing the Laplace transform (t-4)* -H(t-4) to the rule L[f(t-a)H(t-a)]you will find that…

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Q: 7. By using the Fourier transform, find a solution for the following problem (P Ju(1, x) = 4u.z(t,…

A: The complete solutions are given below

Q: 1- Determine the Inverse Laplace transform for -2s²-9s +11 1 (S-2) (s + 3) (s + 1) O Option 1 L-1…

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Q: Determine the causal signal x(n) if its z-transform X(z) is given by: (a) X(z) = 1+3:-1 1+3z-1 +2z…

A: As per our guidelines, we are allowed to answer only the first three sub- parts of a multi- part…

Q: By using Laplace transform to solve the IVP: y"-6y' + 9y = 0,y(0) = 2, y'(0) =-4 %3! Then Y(s) is…

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Q: By using the Laplace transform to solve the system (x' 3x-3y+ 2 x(0) = 1 ly' = -6x-t y(0) = -1 We…

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Q: 3. The Laplace transform of the f(t) = t²e-2t cos(3t) is (a) 2(+2)(8² +45-23) (8²+45+13)³…

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Q: Find the laplace transform of ƒ (t) = 2t³ – 6t – 8 -8s³+12s-6 OF (s) = 84 OF (s) 6s³-8s-12 84 ○ F…

A: Given that,  f(t)=2t3-6t-8

Q: show that: n L{t"-1eat} S - a L{t"eat} By using the definition of the Laplace transform

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Q: 3.2 Use the Laplace transform to solve the following system. х" — Зх' + у' + 2x — у %3D 0 x' + y' –…

A: Given The given system is x"-3x'+y'+2x-y=0x'+y'-2x+y=0x0=0x'0=0y0=-1

Q: 1 G(s) = (s + 10)(s + 1) - Find the Z-transform of the system

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

Q: Give the Laplace transform of 2 0 <x and x < 3 (x) = 3<x and x <4 4 4 3x -3s +e3* + 5 3 -4 + 2 e*'s…

A: Inverse Laplace transferom

Q: 10s – 3 - Find the inverse Laplace transform of F(s) s2 – 4 - 17 O f) 23 -2t -e 4 23 4 17 + 4 -2t…

A: I have stated the used formulas in the solution

Q: Give the Laplace transform of 3x f(x): 0 <x and x < 3 -4 3 3x 3 2 + 2 -3s 4 F(s) = + e 3 -3s 15 3 10…

A: Option C is correct.

Q: 3. Solve each of the following IVP by the Laplace transform method: a. y" - 4 y' = 6 e³- 3 e* y(0) =…

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Q: *: Obtain Z-transform for the Followings 1) x(t) = Coswt 2) x(s) (sta)2 3) x(s) = s(s+1)

A: We have to use standard z transforms.

Q: Determine the Laplace transform for s+2 1- F(s) = ln ³+² S-3 O Option 1 3- F(s) = √√s +3-√s-2 Option…

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Q: if 0s1<3 12. Compute the Laplace Transform of K) = - if t2 3 A) 1 B) 1 C) 1 D) +

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Q: Which of the following is the expression to be ob tained when the Laplace transform is applied to…

A: We are given the differential equation :  2y''-3y'-2y=te2t Applying Laplace transform to both the…

Q: Which of the following is the Laplace transform of the solution to the initial value problem x" + x'…

A: We will find out the required Laplace transform.

Q: Which of the following is the Laplace transform of the solution to the initial value problem x" + a'…

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Q: Obtain the Z transform of 10 s(s² +s+2)

A: We are given the Laplace transform fs=10ss2+s+2=51s-s+1s2+s+2=51s-s+12s+122+722-12s+122+722 So,…

Q: Find the transform of the function below. g(t) = (t^2)*sin(2t) A) (16s^2-12) / (s^2+4)^3 B…

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Q: Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 -…

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Q: The Laplace transform of L e-3tt4| is 4 (s + 3)5 3! (s +4)5 4! (s +3)4 4! (s +3)5

A: To find: Laplace transform of  L[e-3tt4].

Q: When using Laplace transform to solve the IVP :Xn = 'n u(x,0)= - x. t>0 Then u]= 1 - SX e a. SX ce…

A: Given ut=ux, -∞&lt;x&lt;∞, t&gt;0, ux,0=-x

Q: Find Z transform for 3 F(t) = t * * F(t) = u(t-2)

A: Given that F(t)=t3 F(t)=u(t-2) We have to find the Z transformation of f(t).

Q: The inverse Laplace transform of F (s) 5s+2 -is s2 (s² –1) %3D □-5-2t+ 특 + 7e 3e 2 3e t O -5 + 2t +…

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Q: 6. The Laplace transform of e^-5t is * O (1/5)-s O (1/s)-5 O 1/(5-s) O 1/(s-5)

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Q: What is the z transform of h(n) = {1, -2, 1} z - 2 + z1 1- 2z-1 + z2 z2 - 2z + 1 а. b. с. d. 1

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Q: 4.45. Determine the initial value of the function f(t) wbose Laplace transform is 4s F(s) =+ 2s + 9s…

A: We have to find the solution.

Q: 7. Let X(s)=- 2s²-s+3 (s+2)(s+1)(s-2) ROC,{s:-1<Re(s) <2}. Determine x( t). be the Laplace transform…

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Q: Find the transform of the given function of s. F(s)=1/2s+16

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Q: 2.) Find the coefficients for the pan r+3 decomposition for f dx in (z-2)(z-1)

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Q: 2. Determine the Laplace transform of f(t)=teªsin(3t) s-4 а. (s2-3s+5)? 6s-12 b. (s2-2s-6)2 s-4 C.…

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Q: Use the Laplace transform to solve the initial-value problem: [y " +5y'+4y=2 e, y(0) =-3, y '(0) =2]…

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Q: Find the laplace transform of ƒ (t) = 2t² + 4t – 5 OF (s) = 5s5+484+4s³ 86 OF (s) -58²-4s+4 83 OF…

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Q: M=15 Find the Z-transform of the function 2(-M)3k + 50 k – 7 (–M)k-2.

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Q: 7. Find the inverse Laplace transform for each of the following: (c) F(s) = 1-s(S+3s) %3D (d) F(s) =…

A: Let the inverse Laplace of a Laplace function F(s) is f(t). Solution for a: Given function is…

Q: • Determine the casual signal x(n) if Its z-transform X(z) is given by: 1+ 3 z-1 X(z) = 1+ 3 z-1 + 2…

A: Consider the given expression. Xz=1+3z-11+3z-1+2z-2 Simplify the function.…

Q: (2) Find Inverse Laplace transform for; 3 1 (1)F(s) = 3 (2)F(s)= s2 +4 (3)F(s)= s (s +1) s (s² +16)…

A: Given:                 Question 4: F(s)=2s2(s+4)                 Question 5: F(s)=1s(s-1s+1)…

Q: 2. Find the inverse Laplace Transform of the following left-sided signals a. X(s)=+2s +3 6s² +…

A: To find the inverse Laplace transform of…