Solutions Manual to Accompany Ordinary Differential Equations by Greenberg Michael D.;

Author:Greenberg, Michael D.;
Language: eng
Format: epub
Publisher: Wiley
Published: 2014-08-22T16:00:00+00:00

SOLUTION. det(A – λ I) = λ2 + 4 = 0 gives λ = ± 2i, each of multiplicity 1. so Thus, we have the 1-dimensional eigenspace This time we obtain the 1-dimensional eigenspace

Example 3. (Computer) Use Maple to find the eigenvalues and eigenvectors of the matrix given above in Example 1, part (e).

SOLUTION.

with(LinearAlgebra):

A :=Matrix([[1, 2, 3], [1, 2, 3], [1, 2, 3]]):

Eigenvectors(A)

(1)

The print format is this: The first column vector has as its entries the eigenvalues of A, each one shown as many times as its multiplicity. Then, the columns of the matrix that follows are eigenvectors associated with the corresponding eigenvalue. In this example, we see from the output that λ1 = 0 is of multiplicity two and that it has the 2-dimensional eigenspace

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