Use MATLAB to determine the eigenvalues and eigenvectors for the matrix

A = [.5, 0, 5, .5; 0, .8, .8, 1; 0, 0, 1, .9; 0 1 1 0 ]

If b = (3 0 0 0)^T , will we have lim k A ^k b = 0?

Why or why not?

Find A¹⁰b and A²⁰b.

Determine another vector c 0 that is not a multiple of b, such that lim k A^k

Note that choice for c is not unique. Explain your choice for c and calculate A¹⁰c and A²⁰c.

Note: You should not construct an m-file for this assignment. I only need your diary. You may write your answers to the open ended questions on a separate sheet of paper or on the sheet with your diary.