Question

I am getting the incorrect answer for determining the eigenvectors of a matrix. I will post my work in the next post.

Answer 1

eugene vectors are such that:

Ax = Ix, or succinctly; (A-I)x = 0

and im sposing we start with the characteristic equation of A-I ... if memory serves

Answer 2

curious on what your matrix is tho :)

Answer 3

The matrix in question is
\[\left[\begin{matrix}1 & 2 \\ 2 & 3\end{matrix}\right]\]

It's easy to work out the eigenvalues with the formula \[\left| A - \lambda I \right| = 0\]

They are \[2+\sqrt{5}\] and \[2-\sqrt{5}\]

However, when I try to determine the eigenvectors, I get the wrong answer. Please note that the eigenvectors are unit vectors, so we can use \[v _{1}^{2} + v_{2}^{2} = 1\]

The correct eigenvectors are \[\left[\begin{matrix}.5257 & .8507 \\ -.8506 & .5257\end{matrix}\right]\]

Attached is my work which gives me the incorrect answer. I would like to understand what I'm doing wrong.

Answer 4

Where do the values \(2+\sqrt{5} \text{ and } 2-\sqrt{5}\) come from?

Answer 5

Sorry, too lazy to use LaTex. Solving the last line should give the value of lambda. Is this what you did?