The professor teaching a class I am taking wants me to find the eigenvalues and the eigenvectors for the following matrix below.
$$\begin{bmatrix}-5 & 5\\4 & 3\end{bmatrix}$$
I have succeeded in getting the eigenvalues, which are $\lambda= \{ 5,-7 \}$. When finding the eigenvector for $\lambda= 5$, I get $\begin{bmatrix}1/2\\1 \end{bmatrix}$. However, the correct answer is $\begin{bmatrix}1\\2 \end{bmatrix}$ .
I have tried doing this question using multiple online matrix calculators. One of which gives me $\begin{bmatrix}1/2\\1 \end{bmatrix}$, and the other gives me $\begin{bmatrix}1\\2 \end{bmatrix}$.
The online calculator that gave me $\begin{bmatrix}1\\2 \end{bmatrix}$ explains, that y=2, hence $\begin{bmatrix}1/2*2\\1=>2 \end{bmatrix}$ =>$\begin{bmatrix}1\\2 \end{bmatrix}$.
What I do not understand is, why is y must equal to 2?Is it because there cannot be a fraction in an eigenvector?
from Hot Weekly Questions - Mathematics Stack Exchange
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