How to Find Eigenvalues and Eigenvectors for 2x2 Matrices?

[richard7893]

Homework Statement

im trying to find the eigen vector for these 2 matrices: A=[0,0;0,8] AND A=[-8,0;0,0]

Homework Equations

The Attempt at a Solution

BACICALLY WHAT IM DOING IS "GUESSING" AT What x1, is then I am coming up wth the solution to x2 once I've made my guess for x1. how can i know for sure if my guyess is correct?

 

[Pengwuino]

What do you mean by your guesses? Finding eigenvectors and eigenvalues is a process that doesn't need guessing.

 

[HallsofIvy]

Also what do you mean by "the eigenvector for these matrices". Each matrix has two (obvious) eigenvalues and an infinite number of eigenvectors. Do you mean "find the eigenvectors of each matrix" or "find a vector that is an eigenvector for both matrices"?

 

[richard7893]

I mean find the eigenvectors of each matrix. The original question is Find the eigenvals and eigenvecs of A=[1,0;0,9]. I know the eigvals are 1 and 9. However when I try to find the eigvec for lamda =1 and lamda = 9 respectively i get these matrices: when lamda =1 [0,0;0,8] and lamda =9 [-8,0;0,0]. For some reason I'm just thinking that eigenvector for both of these is 0 becase for instance in the mathrix when lamda =1 you get the eqn:
0x+8y=0 and 0x+0y=0. This is almost the same case for when lamda = 9. How do you find x and y to get the eigenvectors without them being 0 because there is no such thing as a 0 eigenvector.