Find a basis for the vector space P3 composed of eigenvectors of the linear transfor- mation T . Then find a matrix representation of T relative to this basis

Find a basis for the vector space P₃ composed of eigenvectors of the linear transfor- mation T . Then find a matrix representation of T relative to this basis.

T : P₃ → P₃,     

T (a + bx + cx² + dx³ )= (a + c + d) + (b + c + d)x + (a + b + c)x² + (a + b + d)x³