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. \begin{align*} -x_1+5x_2&=-8\\ -2x_1+5x_2+5x_3+2x_4&=9\\ -3x_1-x_2+3x_3+x_4&=3\\ 7x_1+6x_2+5x_3+x_4&=30 \end{align*}