Question

Help with eigenvectors.

Answer 1

@dan815

Answer 2

Have can I show this matrix
\[\left[\begin{matrix}1 & 2 & 3\\ 2 & 4 & 6 \\ 3 & 6 & 9\end{matrix}\right]\]
has the following eigenvectores
\[v1=\left(\begin{matrix}-2 \\ 1 \\ 0\end{matrix}\right) \]
\[v2=\left(\begin{matrix}1 \\ 2 \\ 3\end{matrix}\right)\]
\[v3=\left(\begin{matrix}3 \\ 6 \\ -5\end{matrix}\right)\]

Answer 3

a vector \(v\) is an eigenvector of a matrix \(A\) iff \(Av=\text{constant} \times v\).
Compute the three products and it should be clear.

Answer 4

example, your matrix (noted \(A\)) times \(v_1\) is
\[
\begin{pmatrix}
-2 + 2\\
-4 + 4\\
-6 + 6\\
\end{pmatrix}
= \begin{pmatrix}0\\0\\0\end{pmatrix} = 0\times v_1
\]
Do the same with the other vectors.