Find the general solution of x1? = x1 ? 2x2, x2? = 2x1 x2 using the eigenvalue method. do not use complex exponentials in your solution.

Question

04-04-2017
Mathematics

contestada

Find the general solution of x1? = x1 ? 2x2, x2? = 2x1 x2 using the eigenvalue method. do not use complex exponentials in your solution.

Respuesta :

Otras preguntas

The amount of money that is left in a medical savings account is expressed by the equation y=-24x+379, where x represents the number of weeks and y represents t

Help me with this please

Questioning whether an error of law was made at the trial court level is called a/an

Help I truly don’t understand anything

The only political system that could guarantee the cooperation between the legislative and executive branch is

At one time, the Texas Junior College Teachers Association annual conference was held in Austin. At that time a taxi ride in Austin was $1.15 for the first 1/5

1. _ listo porque _ preparado. _ listo porque _ inteligente. a. estoy, soy, estoy, soy b. estoy, estoy, soy, soy c. soy, soy, estoy, estoy d. Soy, estoy, soy,

Why did populists support william jennings bryan?

An organized way to gather information is called

I need a reference on the internet that is related to Greek mythology ty

LammettHash LammettHash · Answer 1 · 2017-04-04T19:34:34+02:00

Guessing on how the system is expressed:

[tex]\begin{bmatrix}x_1\\x_2\end{bmatrix}'=\begin{bmatrix}1&-2\\2&1\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix}[/tex]

The coefficient matrix has eigenvalues [tex]\lambda=1+2i[/tex] with corresponding eigenvectors [tex]\begin{bmatrix}\pm i&1\end{bmatrix}^\top[/tex]. This means the characteristic solution is

[tex]\begin{bmatrix}x_1\\x_2\end{bmatrix}=Ce^{(1+2i)t}\begin{bmatrix}i\\1\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x_1\\x_2\end{bmatrix}=Ce^t(\cos2t+i\sin2t)\begin{bmatrix}i\\1\end{bmatrix}[/tex]
[tex]\begin{bmatrix}x_1\\x_2\end{bmatrix}=C_1\begin{bmatrix}-e^t\sin2t\\e^t\cos2t\end{bmatrix}+C_2\begin{bmatrix}e^t\cos2t\\e^t\sin2t\end{bmatrix}[/tex]