Two linearAlgebra and probability question. The two questions in the attachments, show the steps.

Here is a matrix:

-2

3 4

1 4

A=

-1

2 6

-1

Here is what you need to do:

(a) Give the characteristic equation for this matrix.

(b) Find all the eigenvalues & eigenvectors

(c) Give the diagonalization of the matrix.

(d) Find A20. (Hint: use your diagonalization.)

Show all your work

—

BE NEAT — and upload as a pdf.

Here is an internet:

A.

B.

с.

E

Here is what you need to do:

(a) Add probabilities to the transition diagram, and make a guess:

Which “site” is most important?

(b) Give the transition matrix.

(c) Give the characteristic polynomial—do not attempt to solve it.

(d) Find the eigenvector for the eigenvalue = 1.

(e) Give the PageRank vector (simplified algorithm, i.e., no

damping). Was your guess correct?

Show all your work

BE NEAT– and upload as a pdf.