Let A be a square matrix defined by ( A = egin{pmatrix}-2&-1&-5\ 2&2&3\ 4&2&2end{pmatrix} )
(a) Find the characteristic polynomial of A.
(b) Find the eigenvalues and eigenspaces of A.
(c) Show that A is not diagonalizable, but it is triangularizable, then triangularize A.
(d) Find the three real sequences ( (a)_n, (b)_n ,(c)_n ) satisfying.
( egin{cases}a_{n+1}=-2a_n-b_n-5c_n hspace{2mm},a_0=1 & quad \b_{n+1}=2a_n+2b_n+3c_n hspace{2mm}, b_0=0 & quad \c_{n+1}=4a_n+2b_n+6c_n hspace{2mm},c_0=1 & quadend{cases} )
