Can anyone please check my work and answer for this math problem?

[Math100]

Homework Statement

Is [-1+sqrt(2), 1] an eigenvector of [2, 1; 1, 4]? If so, find the eigenvalue.

Relevant Equations

None.

Can anyone please confirm and check my work with answer because I'm not 100% sure if my work with answer is 100% correct. The question is asking if the given vector is an eigenvector and I've answered no. What's the correct answer for this problem? It's Yes or No?

 

[etotheipi]

I think you need to write a little bit larger. Got any A3 nearby?

 

[Math100]

Sorry, I don't understand. What do you mean about A3 nearby?

 

[etotheipi]

Nevermind, it was just a bad attempt at humour. As for your question, is the vector $\begin{pmatrix} 2\sqrt{2} - 1\\ \sqrt{2} +3 \end{pmatrix}$ a scalar multiple of the vector $\begin{pmatrix} \sqrt{2} - 1\\ 1 \end{pmatrix}$?

 

[Math100]

I think the answer is Yes, because (√2-1)(√2+3)=2√2-1. Therefore, it's scalar multiple. Am I right?

 

[etotheipi]

Right. And and if the result is a scalar multiple of the first vector, as in $Av = \lambda v$, then $v$ is an eigenvector. Does that answer your question?

 

[Math100]

Yes. Thank you so much for the help.