Question

Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such that P-TAP =D 300 030 0 3 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 2 0 0 0 3 0 O A 0 1 0 The matrix is diagonalizable, (PD) = 0 0 1 1 0 3 (Use a comma to separate matrices as needed.) O B. The matrix is not diagonalizable 0 0 3 A Question is complete. Tap on the red indicators to see incorrect answers. Similar Question All parts showing caya yazın

Answer 1

Find eigenvalues of the matrix A |A - 11 = 0 0 (3-2) 0 0 0 (3-2) 3 0 (2-2) :: (3 - 2)((3 - 4) * (2 - 1) - 0 x 3) - 0(0 < (2 - 1) - 0 x 0) + 0(0 ~ 3 - (3 - 1) 0) = 0 6- 52 + - 0(0 - 0) + 0(0 - 0) = 0 :: (3-1)(C6 :: (3-2)(6 +22) - o) - 22) - 0(0) + 0(0) = 0 6- 52 +22 (18 - 212 + 812 - 13)-0+0=0 :: (-12 +842- 212 + 18) = 0 :: - (-2)(- 3) (0 - 3) = 0 :: (8 - 2) = 0 or (2 - 3) = 0 or (- 3) = 0 :. The eigenvalues of the matrix A are given by a = 2, 3,

1. Eigenvectors for 1 = 2 3 0 0 1 0 0 A-h1 = 0 3 0 - 2 0 1 0 0 3 2 0 0 1 3 00 2 0 0 0 3 0 0 2 0 0 3 2 0 0 2 1 0 0 0 1 0 0 3 0 Now, reduce this matrix interchanging rows R2 R3 1 0 0 0 3 0 0 1 0 R₂ + R₂₃3 1 0 0 1 0 0 1 0 R2 + R3 - R2 1 0 0 0 1 0 0 0 0

The system associated with the eigenvalue 1 = 2 1_0_0 (A-20 0 10 0_0_0 $ xn = 0,x; = 0 :: eigenvectors corresponding to the eigenvalue 1 = 2 is 0 0 X3 .: . : Let xz = =1 0 =ܢ 0 1

2. Eigenvectors for a = 3 3 00 1 0 0 A-1 = 0 3 0 - 3 0 1 0 0 3 2 0 0 1 3 0 0 3 00 = 0 3 0 0 3 0 0 3 2 0 0 3 0 0 0 11 0 0 0 0 3 - 1 Now, reduce this matrix interchanging rows Ri Rz 0 3 - 1 0 0 0 0 0 0 R, R, -3 1 0 1 3 II * 0 0 0 0 0 0 The system associated with the eigenvalue à = 3 X1 0 1 X1 (A - 31) X2 BH 0 0 0 X3 X3 0 0 0

1 5 x2 - 33 - 0 + x = 3*3 xx- * eigenvectors corresponding to the eigenvalue a = 3 is ܆܇ = 3'3 x3 Let xn = 1,13 = 2 ܘ ܘ - Let x, = 0, xz =1 0 . 3

2. The eigenvectors compose the columns of matrix P 0 1 0 ..P= 0 0 1 0 1 1. The diagonal matrix D is composed of the eigenvalues 2 0 0 ..DE 0 3 0 0 0 3
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