Let A be the coefficient matrix of the system of equations below. Is A nonsingular or singular?

Question:

Let A be the coefficient matrix of the system of equations below. Is A nonsingular or singular? Explain what you could infer about the solution set for the system based only on what you have learned about A being singular or nonsingular.
- x1 + 5x2 = - 8
- 2x1 + 5x2 + 5x3 + 2x4 = 9
- 3x1 - x2 + 3x3 + x4 = 3
7x1 + 6x2 + 5x3 + x4 = 30