Question

Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (11.22) = STEP 2: Find the eigenvectors Xi and X2 corresponding to 1, and 12, respectively. X1 = X2 - STEP 3: Since the matrix does not have ---Select-- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.

Answer 1

-4 A dod (1) eigen A are I, 1, 2 nalus of Then (d, dz ) = (1, 2) (2) eigen rector se corresponding to x, =) (A - I) X, = 0 7 is 6 7481-10 -4 Y + 2z = 0 3 z co Z 20 4 y to Z EO x is arbitarakey Thus (6) is only eigen vector amesponding to t=1

to 22=2 2 dr with respect eigen rector & [A-21] X2 ro 22 -4 2. 에 y d O o z 25 -10Z -X-49 tez co y t3 z to » Ty=32 Then eigen in rector to 22 =2 -10 is 3 Corresponding oll Since the matrix does not have rectors Three linearly independent eigen Thes Matrixe i's is not diagonalizable.