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

• Math100

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

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

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}##?

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

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.

• etotheipi