Page 162 - Schaum's Outline of Differential Equations

CHAP. 16] e At 145

which have as their solution

Substituting these values into (_/) and simplifying, we have

At
16.8. Establish the necessary equations to find e if

Here n = 6, so

and

The eigenvalues of At are A,j = A^ = ^3 = t, X 4 = X 5 = 2t, and Xg = 0. Hence, X = f is an eigenvalue of multiplicity
three, X = 2f is an eigenvalue of multiplicity two, and X = 0 is an eigenvalue of multiplicity one. It now follows from
Theorem 16.2 that

or, more simply,