Problem 3. Let P2 be the vector space of polynomials of degree 2 equipped with the inner product >= † p(x)}q(x) dr. S = Let W be a subspace of P2 generated by the polynomial x 1. Find an orthogonal basis of the orthogonal complement of W.
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- Use Laplace transform to solve I.V.P x = (-2 23 ) x, X(0) =4. (9 points). Functions y₁ and y₂ are solutions for the corresponding homogeneous equation of the following differential equation. ty" - (1+t)y' + y = t²e²t, t>0; y₁ = 1+t, y₂ = et. a) Use the Variation Method to find a particular solution of the equation. b) Write the General solution of the equation. c) Determine the solution for the differential equation that satisfies initial values y(1) 0 and y' (1) = 4.1 2-Binomial Coefficients: Problem 8 (1 point) What is the coefficient of ¹¹ in the expansion of (x + 2)¹2+x²¹(x+3) ²²?
- 1. Using a Taylor table, derive a finite-difference approximation to the first аф derivative (0%) at i using the grid points i −2, i −1, i, and i + 1.Consider the problem of calculating the median m of the following numbers: 4,5,9. (a) Write down the linear program that you could solve, to find the median m. Then put this LP in the form: min c^T x s.t. Ax 2 b, x 2 0, where x is your list of variables. (b) Now write down the dual of the problem above. Call the list of dual variables y. (Hint: there are 6 components of y.)Answer D and E please