I'm having trouble with this problem :
Give an example for matrix $A$ with these eigenvalues $\lambda_1-1,\lambda_2=1,\lambda_3=0$ while :
$$v_1=(0,1,1)$$ $$v_2=(1,-1,1)$$ $$v_3=(0,1,-1)$$
$v_1,v_2,v_3$ Are eigenvectors of matrix $A$
I don't know how to find matrix $A$ that apply these terms.
The only thing I came up with is that : $$A(\lambda_i)=\lambda_i v_i \rightarrow A(\lambda_i)-\lambda_iv_i =0$$