Find a general solution of the given system using the method (A - [tex]\lambda[/tex]I)V2 = V1.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x'_1 = 2x_1 - 5x_2, x'_2 = 4x_1 - 2x_2[/tex]

[tex]x' =

\left(\begin{array}{cc}2&-5\\4&-2\end{array}\right)[/tex]

characteristic equation:

(2 - [tex]\lambda[/tex])((-2) - [tex]\lambda[/tex]) + 20 = 0

[tex]\lambda[/tex]^2 + 16 = 0

[tex]\lambda[/tex] = 4i

Using this method:

(A - 4i[tex]\lambda[/tex])V_2 = V_1

[tex]\left(\begin{array}{cc}2-4i&-5\\4&-2-4i\end{array}\right) *[/tex] [tex]\left(\begin{array}{cc}a\\b\end{array}\right) = [/tex] [tex]\left(\begin{array}{cc}0\\0\end{array}\right) [/tex]

(2 - 4i)a - 5b = 0

4a - (-2 - 4i)b = 0

When there are no complex roots, I can set a or b = 1 to find the value of the other. And when I row reduce this in my ti89, I get

[tex]\left(\begin{array}{cc}1&i 0\\0&0 0\end{array}\right) [/tex] with a space between the i and 0 in the top row, and the two 0's in the 2nd row.

How do I find a and b in this problem? When I find their values I will have V_1.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Finding a vector associated with an eigenvalue

**Physics Forums | Science Articles, Homework Help, Discussion**