1. eigenvectors

Hey, I'm really struggling today.

We just started doing eigenvectors, and I'm supposed to solve this following problem without using determinants.

Prove that the eigenvectors of the matrix
2 0
0 2
generate a 2-Dimensional space and give a basis for it. Also, state the eigenvalues. I just don't think this stuff is harder than some of the other stuff I've done, but I'm really pathetic right now.

2. The eigenvalues are in your given matrix. ${\lambda}=2$

3. Originally Posted by grandunification
Hey, I'm really struggling today.

We just started doing eigenvectors, and I'm supposed to solve this following problem without using determinants.

Prove that the eigenvectors of the matrix
2 0
0 2
generate a 2-Dimensional space and give a basis for it. Also, state the eigenvalues. I just don't think this stuff is harder than some of the other stuff I've done, but I'm really pathetic right now.
The definition of eigenvalue and eigenvector says that you must have $\begin{bmatrix}2 & 0 \\ 0 & 2\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}= \begin{bmatrix} \lamba x \\ \lambda y\end{bmatrix}$.

Do the multiplication on the left and compare the vectors.