2. Consider the system of differential equations. Determine the eigenvalues and corresponding eigenvectors of the coefficient matrix. dx = 2x+ y dt dy = 4x-y dt answer:

a. Find the eigenvalues and eigenvectors of the matrix x₁ (t) x₂ (t) = X₁ b. Solve the system of differential equations a' = = = V₁ = [₁ 5 -3 4 -2 and X₂ = satisfying the initial conditions V₂ = [₁8] =[3]

a) Write the initial value problem in vector form. b) Solve by using eigenvalues/eigenvectors. c) Write the solution in x(t), y(t) form.

Linear algebra: please correctly and handwritten