Let \( R \) be the row reduced echelon form of a \( 4 \times 4 \) real matrix \( A \) and let the third column of \( R \) be \[ \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix}. \] Consider the following statements: \[ P: \text{If} \begin{bmatrix} \alpha \\ \beta \\ \gamma \end{bmatrix} \text{ is a solution of } A x = 0, \text{ then } \gamma = 0. \] \[ Q: \text{For all } b \in \mathbb{R}^4, \text{rank}[A | b] = \text{rank}[R | b]. \] Then: \\