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
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...
Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for N(A) (the null space of A). Find a basis for RaneA) = C(A) (the range, or column space of A) Problem 2 A matrix A is given by 2 3 0 1 7 2 1 13 16 3 -5 -3 8 22 -1 -1 -11 -18 Find a basis for...
#13 please In Problems 11-14 write the given sum as a single column matrix. 11.4( – 2(2) +(3) -1/ :).. 13. (2)(3) -61 2(2)
1. For the matrix A given below, find col(A) and Nul(A). Also determine if the given vector is in the column space, null space, both or neither. A = -2 -5 1 3 3 11 1 7 8 -5 -19 -13 0 1 7 5 -171 5 1 -3 1 5 1
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
(1 point) Find the eigenvalues and eigenvectors of the matrix A = | -1 (-13 5 -3 11 = , vi = and t2 = ,02 =
3. Find the inverse of the following matrix: (5 pts) B=11 2-3 hy row rednicing the 3x 6 matrices pl 3, where 13 denotes the 3 3 identity nu trix
10. Find the eigen values and eigen vectors of the given matrix 11 30 ( 36)
Find the eigenvalues and eigenvectors of the given matrix. 3 -1 A= 8 -3 Enter the eigenvalues in ascending order. If the eigenvalues are equal, both answers should be the same. 1 11 = -1 X1 = where x1 = (..) ( ) 1 12 = 1 X2 = where x2 =