Question

Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.

Answer 1

step 1: (vede) = (2,3) Answer [as eigen value is diagonal elements for triangular matrix] step-2:- AX-XX Let y = b fa? 2-4 3 2 1 JA-11] 0 03 2a 12a-4b+367 2b + c 1 :6 26 20 30 30 = 2 -> C=0 26 +c=26 6=ki ( let) 2a-46+3 C = 2a → a=kz (tet) 80 Xi = Kz Ki Answer O again, AX2=1242 let X2= 2 -4 3 2 ] 0 2d-4e3f 20 2e +f 3f HO 3d 3e 3f af 34= 3f = f = K3 ( let) 2e +f=3e e-f=K3 2d-4e3f3d d = -4X K3+3x K3 K3 X2 = -K3 K3 = KB [1] Auswer Step3 since the matrix does not have a linearly independent eigen vertors, you can conclude that Camscan the matris iš not diagnozable.