Solving Decimal Eq for Eigen Vectors: vanishing (solving system of linear eqns)

[zak100]

Hi,
I am trying to solve a Eigen vector matrix:

\(\displaystyle \begin{bmatrix}9.2196& 6.488\\4.233&2.9787\end{bmatrix}\cdot \begin{bmatrix}x\\y\end{bmatrix}-\lambda\begin{bmatrix}x\\y\end{bmatrix}=0\)

I have found \(\displaystyle \lambda_1 = 0\) and \(\displaystyle \lambda_2 = 12.1983\)

However, I can't solve the following equations:

\(\displaystyle 9.2196x + 6.488y =0 -------(eq.1)\)

and

\(\displaystyle 4.233x + 2.978y =0 ----(eq.2)\)

I am multiplying \(\displaystyle (eq.1) \) by \(\displaystyle 4.233x\) and \(\displaystyle (eq.2)\) by \(\displaystyle 9.2196\)

Some body please guide me how to solve these equations for \(\displaystyle x\) and \(\displaystyle y\) values.

Zulfi.

 

[HallsofIvy]

Really? Since that matrix does NOT have eigenvalue 0, it has a unique solution and that solution is obviously x= y= 0.

 

[zak100]

Hi,
One eigen value is zero. I cant put the Latex content correctly. I am uploadig the slide so that you can know how they are solving it.

Zulfi.

 

[stapel]

One eigen value is zero. I cant put the Latex content correctly. I am uploadig the slide so that you can know how they are solving it.

To learn how LaTeX works on this site, please try here. Thank you!

 

[zak100]

Hi,
\(\displaystyle \lambda_2 =12.1983\)
I am not able to get the correct answer as shown in the image above.

\(\displaystyle 9.2196x + 6.488y = 12.1983x \)
\(\displaystyle 9.216x - 12.1983x = -6.488y \)

\(\displaystyle \begin{bmatrix}x\\y\end {bmatrix} = \begin{bmatrix}2.7\\1\end{bmatrix}\)

Somebody please guide me how can i get the correct answer?
Zulfi.