# Tricky eigen vectors question

I am trying to find eigen values and eigen vectors for A
Its 2X2 matrix. A first row (16 -10) second row (-10 24)
I got Eigen values as 30.77 and 9.22 but when i try to find eigen vectors here are the equations I end up with
-14.77v1 - 10v2= 0
-10v1 - 6.77v2 = 0

Kinda confused how to proceed with this.

Thanks

Use 9.23, you rounded wrong.

The procedure for finding associated eigenvectors is to find the nullspace of A-&lambda;I. So you have to solve the nullspace of that matrix you wrote up to find the 30.77-eigenspace. Then you'll need to do the process again for 9.23.

Does this clear things up for you? Or do you need help with solving the nullspace? Because that should be easy.

these two equations are not compatible, because you have rounded your eigenvalues, but if you would have used the ratios as an eigenvalued, you'd see that these thwo equations are exactly the same.

When you are solveing for eigenvectors you have to use either of these equation, because they are same, and then if your states are normalizabe, you have to normalize it.

v1^2+v2^2=1

that's your second equation in system!

Hurkyl
Staff Emeritus