Page 382 - A Course in Linear Algebra with Applications

366 Chapter Nine: Advanced Topics

Here the coefficient matrix is

A =

The Jordan form of A was found in Example 9.4.7: we recall
3
the results obtained there. There is a basis of R consisting
of Jordan strings: this is {X, W, Z}, where

X = - 1 , W = 0 and Z

Here AX = 2X, AW = 2W + X, AZ = 2Z.
The matrix which describes the change of basis from
{X, W, Z} to the standard basis is

By 6.2.6 the matrix which represents the linear operator aris-
ing from left multiplication by A, with respect to the basis
{X,W,Z}, is

S^AS = J

Now put U = S X Y, so that Y = SU and the system of
1
equations becomes U' = S~ ASU = JU, that is,

u[ = 2ui + u 2
u' 2 = 2u 2
U'o = 2u 3