Consider the following system. dx dt dy dt Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) λ = = 2x + 3y K₂ Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K₁ = 6x + 5y Find the general solution of the given system. (x(t), y(t)):

Consider the following nonhomogeneous system. dx = 5x + 9y + 5, dt dy = -x + 11y + 15 dt Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) A = 8 Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. If there is only one repeated eigenvalue, enter the eigenvector in each answer blank.) K, = (2,1) K, = Find the general solution of the given system. x() - cge (31) + cge(2+3/1+ 1) + (-) 5 X(t) = 4. 4. Need Help? Read It Watch It

Suppose that the matrix A has the following eigenvalues and eigenvectors:

Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = -i ,7₁ = b. Find the real-valued solution to the initial value problem [y{ ly/₂2 -3 *'-[-D y' = 5 3 Use t as the independent variable in your answers. y₁ (t) = y2 (t) = = = , and A₂ = -3y₁ - 2y2, 5y₁ + 3y2, , 7₂ = y₁ (0) = -5, Y2(0) = 10. 18