For each of the matrices in Exercises 1 through 6, find an orthonormal eigenbasis. Do not use technology.

M303 Section 5.3 Notes- Diagonalization 12-7-16 Recall diagonal matrix- only (possible) nonzero entries are on diagonal o Ex. Simple to compute powers 5 0 2 5 0 5 0 52 0 [0 3] = [0 3 0 3 ]= [ 2] 3 2 02 3 3 [5 0] = [5 0 ] [5 0]= [5 0 ][5 0]= [5 0 ] 0 3 0 3 0 3 0 3 2 0 3 0 33 5 0 5 0 [0 3] = [0 3] o Commute in multiplication Not all matrices can be diagonal, but class of diagonalizable matrices exists that has many of same properties of diagonal matrices o × matrix diagonali