[18 Point Problem 5: Consider the following (2 x 2) matrix A: 1-4 -1] A= 13...
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A = 18] (The 3 -7 same as in the previous problem.) di = 2, V1 = [1] and 12 = -1, V2 = - [11] [1] 3 21 = 1, V1 = ܒܗ ܟܬ and 12 = -2, V2 = 2 x = 1, V1 = and 12 = -2, V2 = [11 11 x = -2, Vi and 12 = -3, V2 [1]
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and corresponding eigenvectors vand v- 1? a. is a 2x2 matrix with repeated eigenvalue λ = 0 with defect 1 (has only one linearly independent eigenvector, not two.) and corresponding eigenvector vi- 13 (5 pts) Which of the direction fields corresponds to the system x -Cx, where...
(1 point) Find the eigenvalues and eigenvectors of the matrix A = | -1 (-13 5 -3 11 = , vi = and t2 = ,02 =
8. Find a symmetric 3 x 3 matrix with eigenvalues 11, 12 , and , 13 and corresponding orthogonal eigenvectors vi , V2 , and V3 1 11 = 1, 12 = 2, 13 = 3, vi -=[:)--[:)--[;)] 1
Consider the matrix: 15 9 13 2 6 10 14 3 7 11 15 4 8 12 16 a- Find the eigenvectors of this matrix and their corresponding eigenvalues. b-Indicate if there are any degeneracy, and if so, change only one element of this matrix to remove this degeneracy (of course you need to recompute the eigenvalues to show that the degeneracy was lifted). Write a Mathematica program to calculate the roots of the following function f(x) = 0.5*e*-5*x+2 using...
Problem 3 The Hamiltonian of a rotator is given by where 11 and 13 are moments of inertia, and Ly, Ly, and L, are the compo- nents of the orbital angular momentum operator. 1. Determine the eigenvalues of the Hamiltonian and their degeneracy in the two limits 11 = 13 and 11 > 13. 2. Sketch the energy spectrum in these two limits. 3. What is the energy spectrum in the limit 11 > 13? Problem 4 Consider the hermitian...
6: Problem 5 Next Prev Up (1 pt) The matrix [ 55 35 A= 91 -57 has complex eigenvalues, A1,2 = a ± bi, where a = and b = The corresponding eigenvectors are v1,2 ct di, where c ) and d ( ( ).
Section 6.1 Eigenvalues and Eigenvectors: Problem 18 Previous Problem Problem List Next Problem (1 point) Find the eigenvalues and eigenvectors of the matrix A = || ao | 10 and
Section 7.6 Complex Eigenvalues: Problem 5 Previous Problem Problem List Next Problem (1 point) Consider the initial value problem date [10 ] x x(0) = [2] (a) Find the eigenvalues and eigenvectors for the coefficient matrix. X = * , ū = (b) Solve the initial value problem. Give your solution in real form. x(t) = Use the phase plotter pplane9.m in MATLAB to answer the following question An ellipse with clockwise orientation 1. Describe the trajectory
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 = . and 12 = V2 = b. Find the real-valued solution to the initial value problem = -3y - 2y, 5y + 3y2 (0) = -11, y (0) = 15. Usef as the independent variable in your answers. y (t) = (1) =