I have a question asking me to "find the eigenvalues and provide the basis of each eigenspace."
I don't have what an "eigenspace" is in my notes (we haven't talked about it in our lectures) and it's not in my textbook, either.
Could someone please explain what they're looking for?
for instance, if you find that the eigen vectors are of the form then is the basis, it is the solution vector without the parameter (you factor out the parameters)
Okay, so my eigenvalue is 1. It has multiplicity 3.
After plugging in my eigenvalue, I find all three rows are equal, so I cancel out two of them. I'm left with:
I find the eigenvector to be:
The question asks for the eigenvalue (which is 1) and the eigenspace. I still don't understand what the eigenspace is? It also has room for two different answers (of 3 rows and 1 column.)
I tried entering but it rejected it.