Determine if each of the statements below is True or False. If it’s True, explain why. If it’s False explain why not, or simply give an example demonstrating why it’s false. A correct choice of “True” or “False" with no explanation will not receive any credit.

3.1 If a 3 × 3 system has infinitely many solutions, then its augmented matrix must have a row of 0’s.

3.2 Consider a system with m equations, n variables, and rank r. Suppose that r = m. If the system is consistent, then it must have a unique solution.

3.3 Again, consider a system with m equations, n variables, and rank r. Suppose that m < n. If the system is consistent, then it must have infinitely many solutions.

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