-57 26] The matrix has eigenvalues \1 = -5 and X2 = 8. Find eigenvectors -130 60 corresponding to these eigenvalues. v1 = [8] and v2 = help (matrices) Find the solution to the linear system of differential equations x' = -57x+26y satisfying the initial conditions x (0) y' = -130x + 60y = 1 and y(0) = 1. x(t) = = help (formulas) y(t) = help (formulas) Book: Section 3.4 of Notes on Diffy Qs

Find the eigenvenctors to this matrix

When I multiplied I got -28+7i+i^2, where i is the eigenvalue

x'(t) = of the any - 2 5-6 4 1-4-6|x (t) x (0) = -2 + -3 1 The only eigen value of this matrix is -3, a triple root. You must explicitly find matrix involved, with the exception cannot involve Also, your answer 0 imaginary any matrix inverses. number i.

Consider the system of differential equations x = -16x1+8x2, x2 = 20x1+8x2. Rewrite this system as a matrix equation ' = Ax. =1 = help (matrices) Compute the eigenvalues of the coefficient matrix A and enter them as a comma separated list. help (numbers) Book: Section 3.4 of Notes on Diffy Qs

Find the eigenvalues and eigenvectors for the coefficient matrix.

a) Find the eigenvalues of A. b) Find three linearly independent solutions of x' = Ax. c) Find the exponential e^(tA) Let A = 2 -1 ا دیا 0 0 3 0 -30

- find the eigenvectors of the diagonal matrix (A) J where. 2 5 0-12 2 4 10 A = and P=[^}; 2 1 5 4 ♡ 1

Suppose a system of differential equations yields eigenvalue λ=1+3i with 2+i eigenvector = Find any real-valued solution.

Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. (-3+i) A₁ = 1 , vi b. Find the real-valued solution to the initial value problem [{ and A₂ = -3y1 - 2/2, 591 +33/2, Use t as the independent variable in your answers. vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5) 32(t)= (5-5/2)^(-it)+(5+5/2)^(it) 4 vo = 3/1 (0) = 6, 3/2 (0) = -5. (-3-1)/