# Math Help - Eigenvalues help

1. ## Eigenvalues help

Hello, I'm having a little trouble solving this question:
"Let A have 0,3 and 5 as eigenvalues and the independent eigenvectors u, v and w.Find a particular solution to Ax=v+w.Find all the solutions."
Could you guys give me a hint or solve it?Thanks

2. ## Re: Eigenvalues help

Hint:

$A\left(\frac{1}{3}v+\frac{1}{5}w\left)=\frac{1}{3} Av+\frac{1}{5}Aw=\frac{1}{3}3v+\frac{1}{5}5w=v+w$

that is, $x=\frac{1}{3}v+\frac{1}{5}w\left$ is a particular solution. Try the rest.