Linear Algebra Questions

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.