5. Solve the linear systems using eigenvalues and eigenvectors. dx -= x + 4z dt dy = 2y dt dz dt = 3x+y-3z

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.

please help with this problem. Should I treat every component as constant?

Apply the eigenvalue method to find a general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. x', = - 2x, + 8x2. x'2 = 12x, - 6x2 What is the general solution in matrix form? x(t) =O

HELP PLEASE!

Consider the linear system dx₁ dt dx₂ dt = 4x1 - 3x₂ = 3x1 + 4x2. 1. Show that upon conversion to the form X'= AX, the eigenvalues of A are complex. 2. Find the general solution of the system.

Show your work

please send complete handwritten solution Q2

Please help me this question! Thank you so much!

dy dy +3 dr? 6. Consider the second-order equation - 10y = 0. di (a) Convert the equation to a first-order, linear system. (b) Compute the eigenvalues and eigenvectors of the system. (c) For each eigenvalue, pick an associated eigenvector V, and determine the solution Y(t) to the system. (d) Compare the results of your calculation with the results that you obtained when you used the guess-and-test method in Homework 6, question 4.