DEFINITION Let A be an n x n matrix. Any values of A for which Av = Av has nontrivial solutions v are called eigenvalues of A. The corresponding nonzero vectors v are called eigenvectors of A. 1 1 -2 -6 1 = 3, v = (2, 1, –1), A = -2 2 -5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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use Equation in the picture to verify that λ and v are an eigenvalue/eigenvector pair for the given matrix A.

 

DEFINITION
Let A be an n x n matrix. Any values of A for which
Av = Av
has nontrivial solutions v are called eigenvalues of A. The corresponding nonzero
vectors v are called eigenvectors of A.
Transcribed Image Text:DEFINITION Let A be an n x n matrix. Any values of A for which Av = Av has nontrivial solutions v are called eigenvalues of A. The corresponding nonzero vectors v are called eigenvectors of A.
1
1 -2 -6
1 = 3, v = (2, 1, –1), A =
-2
2 -5
Transcribed Image Text:1 1 -2 -6 1 = 3, v = (2, 1, –1), A = -2 2 -5
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