To find the eigenvalues, computedet3 − λ 0 0−3 4 − λ 90 0 3 − λ = (3 − λ)(4 − λ)(3 − λ).So the eigenvalues are λ = 3 and λ = 4.We can find two linearly independent eigenvectors301 ,130 corresponding to the eigenvalue 3, and oneeigenvector010 with eigenvalue 4. The diagonalized form of the matrix is3 0 0−3 4 90 0 3 =3 1 00 3 11 0 03 0 00 3 00 0 40 0 11 0 −3−3 1 9 .Note that if you chose different eigenvectors, your matrices will be different. The middle matrix should haveentries 3, 3, 4 in some order, and you should multiply out the product to make sure you have the right answer.

Let A be a 3 × 3 real symmetric matrix and have eigenvalues λ1 = 2, λ2 = λ3 = 1. The eigenvectors corresponding to λ2 = λ3 = 1 are respectively given by v2=(1,0,1), v3=(1,2.-1),Find the eigenvector of A corresponding to λ1 = 2 and the matrix A

For each of the following matrices, and eigenvalue λ has been given.[ 0 4−1 5], λ = 4(a)[2 22 −1], λ = −2(b)3 1 −10 1 24 2 0, λ = 3(c)Find one eigenvector corresponding to the given eigenvalue

Find the Eigen values and corresponding linearly independent Eigen vectors.1.4 6 61 3 21 4 3       

Determine the eigenvalues of the matrix[ 3 1 ] [1 2 ]

a) Find the eigenvalues and the associated eigenvectors of the matrixA = [7 0 −3−9 −2 318 0 −8]