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how do I find eigenvectors (2x2) matrix?

3 -2
0 4
-----------------------------------
eigenvectors are 3 and 4
when placing lamda 3 in the matrix we get

0 -2
0 1

what is the next step for solving eigenvector

The answer, according to the book, is (1, 0)
(edited 9 years ago)
Original post by reb0xx
3 -2
0 4
-----------------------------------
eigenvectors are 3 and 4
when placing lamda 3 in the matrix we get

0 -2
0 1

what is the next step for solving eigenvector

The answer, according to the book, is (1, 0)


do you mean eigenvalues (lambda) are 3 and 4?

Also you stated the nullspace incorrectly:

since lambda is an eignevalue of the 2x2 matrix [A] if:

det{lambda x (identity matrix) - [A]} = 0


So the eigenvectors (assuming non-zero) to be solved are given by:

A x (eignevector) = lambda x (eignevector)

lambda x (eignevector) - A x (eigenvector) = 0

(lambda x identity x eigenvector) - A x (eigenvector) = 0

[(lambda x identity) - A] x eigenvector = 0

i.e.

Eigenspace = Nullspace x {lambda x identity) - [A]} ..........(1)

CASE lambda = 3

sub in (1) gives:

|0 2|
|0 -1| x eigenvector = 0 (be very careful of signs)

The rest is too tedious to run a tutorial.

I direct you to this website for a full description of the process:

[video]http://www.khanacademy.org/math/linear-algebra/alternate_bases/eigen_everything/v/linear-algebra---finding-eigenvectors-and-eigenspaces-example[/video]

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