- #1

PandaGunship

- 6

- 0

## Homework Statement

Let T:P

_{2}→P

_{2}be defined by

T(a

_{0}+a

_{1}x+a

_{2}x

^{2})=(2a

_{0}-a

_{1}+3a

_{2})+(4a

_{0}-5a

_{1})x + (a

_{1}+2a

_{2})x

^{2}

1) Find the eigenvalues of T

2) Find the bases for the eigenspaces of T.

I believe the 'a' values are constants.

## Homework Equations

None.

## The Attempt at a Solution

The problem I am having is actually pulling out the matrix for T. I know how to find eigenvalues (by solving det(λI-A) - A being the matrix) and from that finding the bases of the eigenspaces comes from substituting the eigenvalues into (λI-A) and performing elementary row operations to find the eigenvectors which form the bases.

What I have tried to do is separate the basis (1,x,x

^{2}) from the rest and come up with the matrix :

2a

_{0}-a

_{1}3a

_{2}

4a

_{0}-5a

_{1}0a

_{2}

0a

_{0}a

_{1}2a

_{2}

Am I on the right track here or am I barking up the wrong tree? If so what method should i follow?