Question

Consider the following. List the eigenvalues of A and bases of the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span smallest 2-value has eigenspace span has eigenspace span largest 2-value A3= Determine whether A is diagonalizable. O Yes O No Find an invertible matrix P and a diagonal matrix D such that PAP = D. (Enter each matrix in the form [[row 1], [row 2], ..], where each row is a comma-separated list. If A is not diagonalizable, enter NO SOLUTION.) (D, P) =

Answer 1

Given names Given A=1 1221 [uoi The eigouvdue of 'A' are the Roots 8 the charactishic couchon det (A-11)=0 +1/100 344d-51+2 elll 2 2 - (401 sive - deux - 52+2=0, Eigen dies are 1=1, with multiplicity 8 2 , 1=2 Find the eisau vector for 1=1 solve (A-1):1122i) 211 14o1/ 1400 del 99)+60*) » -4*4254+2 To solve ooo 2 l (400z) ( one Reduce the Matrix : Reduce / 400 OOO The system Associated with the eigen valves. Il (4-15) (9) -(08)3-18). This Reduce to the following system of couction {=0} Isolde { a = 0 } plog into (1) - ( 4 ) , 270 similarly Eisen vector for 1 = 2, are (8) un eigen rector for matrix . are ? (9) on 17-(*), 12-13), 1-10) To Allow diagonalization, the number of eigen vedors must could The Matrix Dimensions There are 2 eigen vedors which is less than 3 and the Matrix cannot be diagonalized - Not Diagonalised No solubion.