Description of eigenvector corresponding to each eigenvalue.

[magimag]

I have a problem I need to solve. I can't find anything in my book that tells me how to do it. It might be worded differently in the book, but I'm not 100% sure how to solve this.

Homework Statement

Give a description of the eigenvectors corresponding to each eigenvalue.

The Attempt at a Solution

The matrix given is A = [1, 3];[-2, 6]

I have found the characteristic polynomial with the equation p(t)=det(A-tI)
the answer for that is p(t)=t^2-7t+12=>(t-4)(t-3)
so the eigenvalues are λ=4 and λ=4

Now I have to give description of the eigenvectors corresponding to each eigenvalue??

 

[Mark44]

I have a problem I need to solve. I can't find anything in my book that tells me how to do it. It might be worded differently in the book, but I'm not 100% sure how to solve this.

Homework Statement

Give a description of the eigenvectors corresponding to each eigenvalue.

The Attempt at a Solution

The matrix given is A = [1, 3];[-2, 6]

I have found the characteristic polynomial with the equation p(t)=det(A-tI)
the answer for that is p(t)=t^2-7t+12=>(t-4)(t-3)
so the eigenvalues are λ=4 and λ=4

Now I have to give description of the eigenvectors corresponding to each eigenvalue??

I would start by finding the eigenvectors, and then maybe you'll be able to describe them.

 

[magimag]

Ok I have found out that the vectors are (1,1) and (3,2)

so could a description be like

x=a(1,1),a≠o and x=a(3,2),a≠o ??

 

[Mark44]

Looks OK except for one thing. The eigenvalues are λ = 4 and λ = 3. Any scalar multiple of <1, 1> is an eigenvector for λ = 4, and any scalar multiple of <3, 2> is an eigenvector for λ = 3.

I would use different scalars for the two eigenvectors, not a for both of them.

 

[magimag]

Ok it was a typo I had it for 3, but ok I thank I got it now then.

thank you :)