Consider the following matrix.A = 23 12 −36 −19Find the eigenvalues and associated eigenvectors of A. (Arrange the eigenvalues so that 𝜆1 < 𝜆2.)

Consider the following matrix.A = 23 12 −36 −19Find the eigenvalues and associated eigenvectors of A. (Arrange the eigenvalues so that 𝜆1 < 𝜆2.)

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

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.

The eigen value of ⎡⎣⎢111111111⎤⎦⎥[111111111]  are

The rank of the following matrix [123246369]⎣⎡​ 123​ 246​ 369​ ⎦⎤​ is