Initial Value Problem, Ordinary Differential Equation: Jordan and Diagonalization
Not what you're looking for? Search our solutions OR ask your own Custom question.
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.
$2.49