The discussion revolves around the concepts of eigenvectors and eigenvalues, particularly in the context of a specific matrix problem. Participants are examining the relationship between eigenvalues, nullspaces, and determinants.
The discussion is ongoing, with participants exploring different interpretations of the eigenvalue problem. Some guidance has been offered regarding the relationship between eigenvalues and determinants, but no consensus has been reached on the specific steps to take next.
There are references to specific matrix operations and the potential complexity of the problem, indicating that participants may be working under constraints related to their current coursework and upcoming topics.
This is simpler than you seem to be making it out to be. If 0 is an eigenvalue, then det(A) = 0, and Ax = 0x for any eigenvector of 0.flyingpig said:Homework Statement
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The Attempt at a Solution
a) Did it already, 3 is the eigenvalue
b) This is just finding the nullspace and the basis of the nullspace are my eigenvectors right?
flyingpig said:c) ignore this one, we cover this next term
You can't just move a bunch of symbols around. You need to do something with your matrix A.flyingpig said:Wait for b)
Ax = λx = 0x = 0
Ax = 0 <=== not nullspace?
Are you implying that
det(Ax) = det(0I) = 0
det(Ax) = 0
How do you pull the x out?