Eigenvalues and Eigenvectors of a 2x2 Matrix P

[SherlockOhms]

Homework Statement

Find the eigenvalues and eigenvectors of P = {(0.8 0.6), (0.2 0.4)}. Express {(1), (0)} and {(0), (1)} as sums of eigenvectors.

Homework Equations

Row ops and det(P - λI) = 0.

The Attempt at a Solution

I've found the eigenvectors and eigenvalues of P to be 1 with t{(3), (1)} and 0.2 with q{(-1), (1)} were t and q are arbitrary (parameters). How do I express the two other vectors (in the question statement) as sums of eigenvectors? Thanks.

 

[vela]

Unless there's another condition you need to satisfy, you can take t=q=1, so the problem is asking you now to solve
$$\begin{pmatrix} 1 \\ 0 \end{pmatrix} = a\begin{pmatrix} 3 \\ 1 \end{pmatrix}+b\begin{pmatrix} -1 \\ 1 \end{pmatrix}$$ which is just a system of two equations and two unknowns. And then do the same thing for the other vector.

 

[SherlockOhms]

Cool. Got it now. Thanks!