Find the eigenvalues and associated eigenvectors of the

Question

Assignment

1. Find the eigenvalues and associated eigenvectors of the given matrix A.

2. The given vectors span a subspace V of the indicated Euclidean space. Find a basis for the orthogonal complement V^⊥ of V .

v₁ = (1,1,1,1,3), v₂ = (2,3,1,4,7), v₃ = (5,3,7,1,5)

3. Solve the initial value problem.

y⁽³⁾ - 2y'' + y' = 1 + xex;   y(0) = y'(0) = 0, y''(0) = 1

4. Apply the eigenvalue method to find a general solution of the given system.

x₁' = -3x₁ + 4x₂,     x₂' = 6x₁ - 5x₂