Find a basis for the vector space $P_3$ composed of eigenvectors of the linear transformation $T$. Then find a matrix representation of $T$ relative to this basis. \begin{equation*} \ltdefn{T}{P_3}{P_3},\quad\lt{T}{a+bx+cx^2+dx^3}= (a+c+d)+(b+c+d)x+(a+b+c)x^2+(a+b+d)x^3 \end{equation*}