List of top Linear Algebra Questions on Linear Transformations (Rank-Nullity Theorem) asked in GATE MA

Let \( P_3(\mathbb{R}) \) be the vector space of all polynomials of degree at most three with real coefficients under usual polynomial addition and scalar multiplication. Let \( T: P_3(\mathbb{R}) \to \mathbb{R}^2 \) be the linear transformation defined as \[ T(p) = \left(p(1), p'(1)\right) \] for all \( p \in P_3(\mathbb{R}) \), where \( p' \) is the derivative of \( p \).

Then the nullity of \( T \) is equal to ______. (Answer in integer)