The discussion revolves around finding the eigenvalues and eigenspace of a given 2x2 matrix, specifically the matrix with entries (3,0) and (8,-1). Participants are exploring the computation of eigenvalues and the corresponding eigenspaces.
Participants are actively engaging with each other's computations and questioning the methods used to find the eigenspace. There is a mix of agreement on the eigenvalues, but confusion remains regarding the eigenspace calculations, indicating a productive exploration of the topic.
Some participants mention specific equations and methods used to find eigenvectors, while others highlight discrepancies in the results obtained, suggesting a need for further clarification on the process of solving (A - λI)x = 0.
Chewybakas said:Homework Statement
Find the eigenvalues and eigenspace of the given vector.
Homework Equations
Matrix = (3,0)
(8,-1)
The Attempt at a Solution
I have determined the eigenvalues to be -1 and 3, but when I try compute the eigenspace when lambda = -1 I constantly get confused and end up with the space equal to span(t[0,0]) tεℝ. Can anyone help or confirm that answer!
Chewybakas said:I reduced the original matrix to reduced row echelon form which gave me the identity 2x2 matrix, which when finding two values v1,v2 where when multiplied by the identity matrix gives zero, I get the answer stated above but when i tried a different way I get the eigenspace 2v1 and 9v1 which again confuses me.