Question

Find the eigenvalues and eigenvetors of the following matrices. Show all your work. T2 5 1 1. A=10-1 61, 2 161 1 -4 2, A=

Answer 1

1. Solution:

0 -1 6 Matrix eigenvalues The eigenvalues of A are the roots of the characteristic equation det(A-λ)-0 det|10-1 61-ん1010 Using the Zero Factor Principle Solve λ_2_ The final solutions to the equation are The eigenvalues are

0 -1 6 Matrix eigenvectors To find the eigenvectors v, solve (A-λ 1)v 0 for each eigenvalue λ Find the eigenvalues for 0 -1 6 Eigenvectors for λ--1: Eigenvectors for-2: 0 17 Eigenvectors for-3: The eigenvectors For-1 6 17

2. Solution:

2 16 1 -4 Matrix eigenvalues The eigenvalues of A are the roots of the characteristic equation det (A-λ)-0 2 16 )一人 -4 det The eigenvalues are:

2 16 1 -4 Matrix eigenvectors To find the eigenvectors v, solve (A-λ 1)-0 for each eigenvalue λ Find the eigenvalues for values for 1 -4 2 16 4, -6 Eigenvectors for4: 2 Eigenvectors for λ -6: 2 16 1 -4 The eigenvectors for (91