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

• Math100
In summary, the conversation is about confirming and checking if a given vector is an eigenvector. The correct answer is determined to be Yes, as the vector is a scalar multiple of the other given vector. The concept of eigenvectors is also briefly discussed.
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

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One way to check if your math problem is correct is to go through each step of your solution and make sure it is accurate. You can also plug your answer back into the original problem to see if it satisfies the equation.

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