Final answer:
a) If the system has three unknowns and R has three nonzero rows, then the system has at least one solution. b) If the system has three unknowns and R has three nonzero rows, then the system can have an infinite number of solutions. c) To determine if the system below has an infinite number of solutions, we need to check if there are any free variables.
Step-by-step explanation:
a) If the system has three unknowns and R has three nonzero rows, then the system has at least one solution. This is because if R has three nonzero rows, it means that there are three linearly independent equations, which is enough to determine the values of the three unknowns.
b) If the system has three unknowns and R has three nonzero rows, then the system can have an infinite number of solutions. This is because having three nonzero rows indicates that there are more equations than unknowns, and when this happens, there can be multiple solutions or an infinite number of solutions.
c) To determine if the system below has an infinite number of solutions, we need to check if there are any free variables. If there are free variables, it means that the system has an infinite number of solutions. To do this, we can put the system into reduced echelon form and see if there are any columns without a leading 1. If there are, then those columns correspond to free variables, and the system has an infinite number of solutions.