Question

(8 points) Solve the system of differential equations x'(t) = [-2 0 1 2 -3 2 -37 1 -4 x(t), x(0) = The only eigenvalue of this matrix is -3, a triple root. You must explicitly find any matrix involved, with the exception of any matrix inverses (in the same way that the solutions were done in class). Also, your answer cannot involve the imaginary number i.

I need it in the Jordan Canonical Form. The solution should look like:

$x(t) = \begin{bmatrix} v1&v2&v3 \end{bmatrix}\begin{bmatrix} e^\lambda ^t & ---& ---\\ & e^\lambda ^t & ---\\ & & e^\lambda ^t \end{bmatrix}P^-^1.b0$

Answer 1

Salutifon: deffecontial gquations = (t), thes matare cigen value -> eigen veds - 3 -3+3 -u+ 3

P9.00:2 → ganeudisad Rgon vectoi (A- x) 92 a+ 2a, = -1 4 choose (A- x2) V Vr ->

F' కి ఇ + 2 : - 1 )(4) ా (3) e ఇ Solition గో Gorenal -st ఆ D): ( - () (ఇ) nco) ి 26,-Ce=3

-2 C2 C-C3=1 C3=/2-1 C3 =-V2 -3t