# Initial Value Problem, Ordinary Differential Equation: Jordan and Diagonalization

Find the solution of the system X' using the "diagonalization" technique (actually the Jordan form in this case)

Please see the attached file.

https://brainmass.com/math/ordinary-differential-equations/initial-value-problem-ordinary-differential-equation-jordan-diagonalization-8096

#### Solution Preview

because,

X' = AX + g

A = = {(a11,a12,a13),(a21,a22,a23),(a31,a32,a33)}

=> A = {(2,0,0),(-1,0,-1),(1,1,2)}

Now,

(A - lI)X = 0

=> determinant (A-lI) = 0

=> l = 1,1,2 (= eigen values) => non diagonalizable

=> eigen vectors = (0,1,-1) for l =1, (1,-1,1) for l = 2 but for ...

#### Solution Summary

The solution to a system expressed as matrices is found. Initial value problems and ordinary differential equations are solved by using Jordan and Diagonalization.

$2.19