Question 2 (Eigenvalue method) Question 2. Find the general solution of the homogeneous linear system below using the eigenvalue method. - (2) y

Question 3 (Eigenvalue method) Question 3. Find the general solution of the homogeneous linear system below using the eigenvalue method. 3- (i) y

Consider the linear system = Find the eigenvalues and eigenvectors for the coefficient matrix. λι and = V₁ = 12 = ປີ2 = [8] [8] help (numbers) help (matrices) help (numbers) help (matrices) Find the real-valued solution to the initial value problem x = -3x1 - 2x2, x = 5x1 + 3x2, x1(0) = 7, x2(0) = −10. Use t as the independent variable in your answers. x1(t) help (formulas) x2(t) = help (formulas) Book: Section 3.4 of Notes on Diffy Qs

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SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer(s) Label them ( C& D)

For the linear system x' = Find the eigenvalues and eigenvectors for the coefficient matrix. λι ×₁ = 0,0₁ = and X2 = [8] [8] help (numbers) help (matrices) help (numbers) help (matrices) Book: Section 3.4 of Notes on Diffy Qs

Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction -Integration

11) Find the values of such that the equations have non-trivial solutions. What are the eigenvalues and eigenvectors? (6-2) x + 3y = 0 3x - (2+2)y = 0

Let 1 A = -2 1 Consider the system of equations = A. (a) Find all eigenvalues of A. (b) Show that 7 = 0 is the only equilibrium solution of the system. %3D (c) Determine whether 7 Ở is a node, or a saddle, or a spiral point. (d) Determine the stability of 7 = 0. 2.

Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion2.