1. **State the problem:** Solve the system represented by the augmented matrix $$\left[\begin{array}{cc|c} 1 & -2 & 7 \\ 0 & 0 & -9 \\ \end{array}\right]$$ using Gauss-Jordan elimination. 2. **Understand the matrix:** The first row corresponds to the equation $$1 \cdot x - 2 \cdot y = 7$$ The second row corresponds to $$0 \cdot x + 0 \cdot y = -9$$ 3. **Analyze the second equation:** The second equation simplifies to $$0 = -9$$ which is a contradiction because zero cannot equal a nonzero number. 4. **Conclusion:** Since the system contains a contradiction, it has **no solution**. **Final answer:** c) No solution