
eigenvector help
hello!
I need help with this question .i dont think i have asked this before.thanks.
Suppose A is n*n matrix and lamda1,2 are eigenvals of A such taht lamda1 is not equal to lamda2.
Let V1 be an eigenvector corresponding to lamda1 and v2 be an eigenvector corresponding to lamda 2.
Prove that v1 and v2 are linearly independent.
How do i go about doing this ?

Re: eigenvector help
Suppose, by way of contradiction, that $\displaystyle v_1$ and $\displaystyle v_2$ are not linearly independent. Then, for some constant c, $\displaystyle \textbf{A}v_1=\lambda_1\textbf{A}$, and $\displaystyle c\textbf{A}v_1=\lambda_2\textbf{A}$. Do you see where this is going? (Wink)