Question 4 Not Marked (a) Provide an example of a linear transformation T₁: P₁ (R) → P₁ (R) such that N(T₁) = R(T₁). (b) Show that there does not exist a linear transformation T₂: P₂ (R) → P₂ (R) such that N(T₂) = R(T₂). (c) Provide an example of a linear transformation T3: P3(R) → P3(R) such that N(T3) = R(T3).

Fig: 1