3. Verify orthogonality for the following ODE and find the eigenvalues and eigenfunctions: (x²)² + (a + 1) == 0 +(a + 1) = 0 y(1) = 0 y(e) = 0 x3
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- Find the eigenvalues and the eigenvectors of A and A-1 (check the trace!): A λι = X2 = 2 A-1 = [ -0.5 11 0.5 ]: λι = with x1 = and 9. with x2 = with x1 = and 9. X2 = with x2 =Find the eigenvalues and the eigenvectors of A and A²: A 1 3 = 2 0 λι 2 = A² = 2 -31 6 λι 2 with X1 and with x2 with X1 ။ = with x2 andFor each of the following ODEs determine if the eigenvalues are (a) real and distinct, (b) repeated, (c) complex conjugate pairs: 1. + 2x + 3x = 0 2. + 4x + x = 0 3. x + 4x + 4x = 0 4. x+3x0
- Find the eigenvalues and eigenvectors for the coefficient matrix.Let A = = [a b]. Find a formula for for the eigenvalues of A in terms of a, b, c and d.R.p Find the eigenvalues and eigenfunctions. Verify orthogonality. Start by writing the ODE in the form (1) [Sturm Liouville].... (y'/x)' + ( λ+1)y/x3 = 0, y(1) = 0, y(eπ) = 0 , * set x = et
- Which of the following are eigen functions of the operator d2/dx2 , find the corresponding eigen value? (i) Sin x (ii) Sin2x (iii) e2xLet A (a) Determine the eigenvalues X₁ and ₂ of A where X₁Consider the linear system X1 = and Find the eigenvalues and eigenvectors for the coefficient matrix. A₂ = 0 JI ← A, V₁ 9 V2 = 81 = = -3 6 - - 4 x. help (numbers) help (matrices) help (numbers) help (matrices) For each eigenpair in the previous part, form a solution of a' = Ax. Use t as the independent variable in your answers.Consider the function T : P2(R) → P2 (R) given by T(a+ bx + cx²) = (a – b+ c) + bx + (-b+2c)x² Find eigenvalues of T and state their algebraic multiplicity.set. Solve eigenveuro Find a particular solution to r' = x – y + et, y = -4x + y+ t using undetermined coefficients. %3DFind the matrix A of the quadratic form associated with the equation. 2x2 - 3xy - 2y2+ 11 = 0 A = Find the eigenvalues of A. (Enter your answers as a comma-separated list.) Find an orthogonal matrix P such that P'AP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ..], where each row is a comma-separated list.) P =SEE MORE QUESTIONS