Page 153 - Schaum's Outline of Differential Equations

136 MATRICES [CHAP. 15

15.12. Find the eigenvalues of A =

We have

Hence,

2
The characteristic equation of A is X - 3X - 10 = 0, which can be factored into (X - 5) (X + 2) = 0. The roots of this
equation are A,j = 5 and X 2 = -2, which are the eigenvalues of A.

15.13. Find the eigenvalues of A? if A =

Then,

2
2
and the characteristic equation of At is X + t = 0. The roots of this equation, which are the eigenvalues of At, are
A,j = it and X 2 = —it, where i = -J-l.

15.14. Find the eigenvalues of A =

Thus,