Consider the linear system dc = 4x + 1.6666666666667y, x(0) = 3 dt dy dt =...
Consider the linear system dc dt = 5x + 2.3333333333333y, x(0) = 4 dy dt = – 2y, y(0) = - 3 If the associated matrix has the form M= с Find the entries. a = Preview Preview b= C= Preview d= Preview Find the trace and determinant of M. Preview tr(M) = det(M) = Preview Find the eigenvalues 11, 12 of M, where li > 12. 21 = Preview 12 = Preview Let vi = [1, yı] be an...
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
(1 point) Consider the linear system -3 -2 333 5 a. Find the eigenvalues and eigenvectors for the coefficient matrix. di = and 12 02 b. Find the real-valued solution to the initial value problem syi ly -341 – 2y2, 5y1 + 3y2, yı(0) = 11, y2(0) = -15. Use t as the independent variable in your answers. yı(t) y2(t)
Section 6.1 Eigenvalues and Eigenvectors: Problem 10 Previous Problem Problem List Next Problem 4 and the determinant is det(A) --- 45. Find the eigenvalues of A. (1 point) Suppose that the trace of a 2 x 2 matrix A is tr(A) smaller eigenvalue larger eigenvalue Note: You can earn partial credit on this problem Preview My Answers Submit Answers Section 6.1 Eigenvalues and Eigenvectors: Problem 8 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues di < 12...
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
(1 point) Consider the linear system 3 2 ' = y. -5 -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 = 15 and 2 V2 b. Find the real-valued solution to the initial value problem Syi ly 3y1 + 2y2, -541 – 3y2, yı(0) = 0, y2(0) = -5. Use t as the independent variable in your answers. yı(t) y2(t)
<Problem 2> Answer the following questions about the square matrix A of order 3: A= III. The square matrix B of order 3 is diagonalizable and meets AB=BA. prove that any eigenvector p of A is also an eigenvector of B. IV. Find the square matrix B of order 3 that meets B2 = A, where B is diagonalizable and all eigenvalues of B are positive. V. The square matrix X of order 3 is diagonalizable and meets AX =...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
Find dy/dt using the given values. y = x - 4x for x = 3, dx/dt = 2. y = [ X dt . dx/dt = 2. Enter an exact number
Problem 2. (a) Let A be a 4 x 4 matrix with characteristic polynomial p(t) = +-12+} Find the trace and determinant of A. 2 e: tr(4) and det(A) = 0 12: tr(A) = 0 and det(A) 2 3 2 T: tr(A) = 0 and det(A) 3 : None of the other answers 01 OW