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fusilli_jerry89

Member

Registered: 2006-06-23

Posts: 86

Linear Algebra Question.

I am having a little trouble understanding this question. Maybe i'm too tired of studying.. Thanks ahead of time!

For each of the linear maps R^2 → R^2, find a basis of R2 consisting of eigenvectors
of the linear map, or explain why this is not possible.

(a) The dilation D : R^2 → R^2 given by D(u) = −3u for all u ∈ R^2

whatismath

Member

Registered: 2007-04-10

Posts: 19

Re: Linear Algebra Question.

Hi, I think you just need to check the definition
of eigenvector.

is an eigenvector
of a linear transformation

(must be endomorphism
or at least finite dimensional space of same dimension)
if

and there exist

(the associated eigenvalue) with

.

So we want here

with

,
or

. Since

,

must be 3. Then

can be ANY non-zero vector (in

).

Hence any basis of

, in particular the canonical basis

, will do.