compute its eigen value and vector
HOW TO FIND THE SECOND EIGEN VECTOR FOR A MULTIPLICITY 2 ? The objective is to find the eigenvalues and corresponding eigenvectors. (2 0-1 1 0 Consider the matrix, A= 0 2 10 4
Sketch the vector function and compute its divergence. 2
question 9. find the eigen value and vector Exercises 3.7 In Exercises 1-12, determine the e-values 4 e-vectors. [ 3-2 4] 5.4-[ -[] 7.1-3, . T 3 -1-1] [i 1-1] [1 1 -2] (9. A = -12 0 5 10. A = 10 2 -1 11. A= 0 2 -1 L 4-2-1) Lo o i Lo o 1 In Exercises 13-18, use condition (5) to determine whether the given matrix Q is orthogonal. 6 67
Problem 2: Find the eigen-value decomposition of the matrix: 1 2 2 A 2 1 2 2 2 1
Problem point Consider the new system and the grand eigen vector for the court , and- Finder on the room 3y + 2y --- (0) (0) -- Use the win your - Note: canon this pro Problem por Find the most per real valued on to the line system of differential equations?
Q1. Consider A = | 2 1 0 | . The eigen values of A are λ1 =-3, λ2 =-1, and λ3 = 3 and the 0 0 -3 corresponding eigen vectors are Let T- vi | v2 l v31. From linear algebra, we know that 0 0 A3 Using this relationship, compute eAt.
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19. Suppose A and B are n xn matrices. a. Suppose that both A and B are diagonalizable and that they have the same eigen- vectors. Prove that AB = BA. b. Suppose A has n distinct eigenvalues and AB = BA. Prove that every eigen vector of A is also an eigen vector of B. Conclude that B is diagonalizable. (Query: Need every eigenvector of B be an eigenvector of A?)
2) In each case below show (in the space provided directly) that F(y) is an eigen- function of the operator A and find the eigen-value a (Hint: Å F(y) = a F(y) ) F(y) Eigen-value d/dy2 Sin ay ii) d/dy elay
4.22. Consider the vibrating system described by 42 -2 1 Compute the mass-normalized stiffness matrix, the eigenvalues, the normalized eigen- vectors, the matrix P, and show that PTMP I and PTKP is the diaggaal matrix of eigenvalues Л 4.22. Consider the vibrating system described by 42 -2 1 Compute the mass-normalized stiffness matrix, the eigenvalues, the normalized eigen- vectors, the matrix P, and show that PTMP I and PTKP is the diaggaal matrix of eigenvalues Л