Skyknight9
New member
- Joined
- Jun 16, 2017
- Messages
- 1
I have trouble finding Basis for Eigenspace. At least half of the time i get a correct answer, but when I run into a complicated problem with 4 x 4 matrix thats when the trouble begins for me. I know how to compute eigen values and row reduce, but my main issue is figuring out geometric multiplicity for eigen value/ eigen space.
For example:
http://slader.com/textbook/97805387...-introduction-third-edition/321/exercises/15/
This is a solution to one of my homework problems. My answer matches everything here except the eigen spaces for eigenvalues of 2 and - 2. The eigen space that I wrote for eigen value of 2 is [1,1,0,0] as opposed to the solution of {[1,0,0,0] and [0,1,0,0]}
As you can see I have 1 vector in my eigenspace as opposed to 2. So how do I know if I have to have 2 vectors in my eigen space and not 1, or 3, or 4 etc.?
If anyone could explain this to me or post a step by step guide to finding basis for eigenspace, id appreciate it
For example:
http://slader.com/textbook/97805387...-introduction-third-edition/321/exercises/15/
This is a solution to one of my homework problems. My answer matches everything here except the eigen spaces for eigenvalues of 2 and - 2. The eigen space that I wrote for eigen value of 2 is [1,1,0,0] as opposed to the solution of {[1,0,0,0] and [0,1,0,0]}
As you can see I have 1 vector in my eigenspace as opposed to 2. So how do I know if I have to have 2 vectors in my eigen space and not 1, or 3, or 4 etc.?
If anyone could explain this to me or post a step by step guide to finding basis for eigenspace, id appreciate it