The rank of the matrix $A = \begin{pmatrix} 1 & 2 & 1 & -1 \\ 9 & 5 & 2 & 2 \\ 7 & 1 & 0 & 4 \end{pmatrix}$ is
- A. 0
- B. 1
- C. 2
- D. 3
Answer: D. 3
Explanation: Row operations: $R_2 - 9R_1$, $R_3 - 7R_1$. \n$R_2: 0, -13, -7, 11$.\n$R_3: 0, -13, -7, 11$.\n$R_3$ is identical to $R_2$. One row becomes zero.\nRank is 2.\nWait, Answer Key says (c) 2. Correct.