Questions:
Eigenvalue and eigenvector of matrix
1. Find all the eigenvalues and corresponding eigenvectors of the matrix A = [ 3 1 ] from example.
[ 1 3 ]
2. Show that V is an eigenvector of A and find the corresponding eigenvalue.
A = [ 1 2] , V = [ 3]
[ 2 1] [ -3]
A = [ 4 -2] , V = [ 4]
[5 -7] [ 2]
3. Show that λ is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue.
A = [ 2 2] ,λ = -2
[ 2 -1]
A = [ 0 4] ,λ = 2
[-1 5]
4. Find all the eigenvalues of the matrix A. Give bases for each of the correspondingeigenspaces. Illustrate the eigenvalue and the effect of multiplying eigenvectors by A.
A = [ 2 4]
[ 6 0]
A = [ 1 2]
[-2 3]