1) a) Find the Laplace transform of the function f(t)=(3tsin 4t +5e* +7t)u, (t); b) Find the poles and zeros of the transfer function given by s* (s+5) G(s)=- and mark them in the s-plane; (s+7)(s² +4s+6) c) Find the inverse Laplace transformation of the function given by 2(s+3) G(s)= s(s²+2s+5)'

Q: Find the transform of the function below. j(t) = 3sinh(2t)+3sin(2t) A 6/(s^2 - 4) + 6/(s^2 - 4) в…

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Q: T: M2x2(R) → R³ is a linear transformation which satisfies 7(: ) ‚T 7(; :) - 7(: )- T „T Determine T…

A: The given transformation is given as: T:M2×2ℝ→ℝ5T1111=10001,T1222=11002T1323=12113,T1324=12324

Q: Determine whether T is a linear transformation. T: Mnn --->R defined by    T(A) = tr(A)

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Q: Linear transformation T'defined by T(x) = Ax %3D 1 -1 0. where A 1 -2 -3 Determine the Ker(T). 1 1…

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Q: Determine the Laplace transform of f (t) = 6e* +e* -9 O 16/s-5)] + [1/(s+3) - 19/s] O 16/(s+5)] +…

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Q: The Fourier transform of a function } (t) iš defihed by F(w) = f(t)e-jwtdt %3D a) Using the above…

A: The Fourier transform of a function f(t) is defined by F(ω)=∫-∞∞f(t) e-jωt dt 1) We have to find the…

Q: Linear transformation T'defined by T(x) = Ax 1 -1 where A 1 -2 -3 Determine the Ran(T). a) Span{ (b)…

A: Given a linear transformation T defined as Tx=Ax, where A=1−101−2−3 We have to determine rangT.…

Q: Determine whether T is a linear transformation. T: Mnn --->R defined by     T(A) = rank(A)

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Q: Find the Fourier Transformation of II (t-) Select one: O l sinc(f) O ef sinc(2f) O jrf sinc(f) 3jef…

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Q: Find the complex transform of F(x) = e¬l\l, –∞ < x < ∞

A: Complex Fourier Transform or Fourier Transform: Let Fx be a function defined on R Then Complex…

Q: Find the Laplace transform of 6e'cos2t - e 6(8– 5) (8 - 5)2+4 8-7 6s В (8 – 5) 2+4 S- 7 s2+4 s-7 (s…

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Q: L{e2"sin2t + etcos3t}

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Q: Let T1 : P2 → R² and T2 : R? → R2x2 be linear transformations defined as follows. a + b b - T1(ax? +…

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Q: Evaluate R(3x+6y)dA where R is the triangle with vertices (0,3), (4,1), and (2,6) using the…

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Q: 12 Integrate: ,V4 - z² + dr

A: The given function is 4-x2+x7+24-x2 We have to integrate this function over the interval -2, 2

Q: True / False. The function L: C'(R) - C(R) defined by L (f) = -f' is a linear transformation.

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Q: бу"" + 5у" + у'%3D0 У (0) %3D — 2, у' (0)%3 2, у" (0) 3D 0

A: We have 6y'''+5y''+y'=0 with initial conditions y0=-2, y'0=2, y''0=0 Now, apply Laplace transform on…

Q: 2) a) Find the Laplace transform of the function f (t)=(3e* cos 4t+ 3te +3)1(t) using related…

A: Given: (a) f(t)=(3e-2tcos4t+3te-4t+3) To find Laplace transform of this function

Q: T(u) = Define the linear transformation T: R² → R³ by T(x) = Ax. Find the images of " = TV) Let II A…

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Q: O Find inverse Z-Transform of 1- 3z-5 (1– 0.2z-1)(1+ 0. 6z-1) X(z) = ving ROC = 0.2 < ]z| < 0.6

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Q: (I) Find the fractional linear transformation f such that f(0) 2 – 2i, f(1) = 0 and f(∞) = -2 – 2i.…

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Q: Find Fourier transform for : A) f(t) = e-3t cos² (3t) B) f(t) = te tu(t - 3)

A: (A)Given f(t)=e−3tcos2⁡(3t).Now, we'll find the Fourier transforms for individual terms.The Fourier…

Q: F: M2x2 → R, given by F(A) = det A; G: M2x2 → M2x2: given by G(A) = A'.

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Q: t+2 1. La transformada de Laplace de la función (2t – 3)e 3 es igual a: a) e 2 2 3 21 S-- 3, 2 2 3…

A: Given that  (2t-3)e^(t+2)/3 To find the Laplace transformation of given function

Q: (3) Consider the linear map T : R? → R² which sends (1,0) → (-3, 5) and (0,1) → (4, –1). (a) What is…

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Q: -21 e * u(t) + e ª u(1)

A: The given function is    e-tut+e-2tut Let xt=e-tut and x1t= e-2tut

Q: An architect designs two houses that are shaped and positioned like a part of the branches of the…

A: Given Equation:- 2025y2-225x2=455,625

Q: Find the Inverse Laplace transform of : 5s-2 s² (s+2) (S-1) a) b) S (s²+a²)(s²+b²)' a² # b², ab # 0

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Q: Let T₁ : R² → R² and T₂: R² → R² be linear transformations defined as follows. T₁ 7) ([2])-[-521+…

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Q: pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way…

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Q: Which of the following transformations T: R² → R³ are linear? Find the image of the vector x =…

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Q: Find the Jacobian of the transformation x - 3u + 7v, y = u² – - v.

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Q: Let. a 3 = (-) = -(1) - P = ( ) 5 and a) Find Fourier Coefficient of b with respect to a . b) Find…

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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: Q4) Q2) t" ( by definition) find Laplace transformation

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