Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 0 -3 9 4 -18 0 4 -4 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix.
0 -3 9
HH
-4 4 -18
0 0 4
(a) the characteristic equation
−(λ −4) (λ − 6) (λ + 2) = 0
(b) the eigenvalues (Enter your answers from smallest to largest.)
(21, 22, 23) = 1
-2,4,6
a basis for each of the corresponding eigenspaces
X₁ =
x2 =
X3 =
Transcribed Image Text:Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 0 -3 9 HH -4 4 -18 0 0 4 (a) the characteristic equation −(λ −4) (λ − 6) (λ + 2) = 0 (b) the eigenvalues (Enter your answers from smallest to largest.) (21, 22, 23) = 1 -2,4,6 a basis for each of the corresponding eigenspaces X₁ = x2 = X3 =
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