Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0 a. )= = cos(2t) + sin(2(t − 4π)µ(t − 4π)

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Q: details] [Justify all your answers in Let W be the set of all vectors 2a + b b-2a -2a + 3b C in R4.…

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Q: 23. 49054081 45082836 If A³ =[ p(2)=2²-92-14 = 0. 90165672 82866208 ] and the characteristic…

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Q: 12. y' = y, y(0) = 1

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Q: Solve the equation x" + 4x = 8(t), x(0)=0, x'(0) = 0 a. x(t)=sin(2t) b. x(t)=[1-e-²¹-2te-²¹] + µ(t −…

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Q: . What is the projection of v=e₁ +2e2 − 3e3 on H : x₁ + 2x2 + 4x4 = 0? . Let V be a subspace of Rn.…

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Q: Define the resultant of two polynomials. Let and P₁(x, y) = 3x² - xy — - 4x + y − 3 P₂(x, y) = x² –…

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Q: Prove or disprove: if A, B, and C are sets, then A- (BNC) = (A - B)U(A-C)

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Q: 3. Find the inverse Laplace transform. a) 8s2 − 4s + 12/s(s2 + 4)

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Q: ∞ -3t Evaluate test sin 3t dt. [Hint: Use the definition of Laplace transform]

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Q: 2. Let A= 101-1 -2 04 02 22-23 1 242 51 a. Find a basis for the column space of A.

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Q: Draw a simple graph that has a Euler circuit, but no Hamilton circuit.

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