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Is each statement true or false? If true, explain why; if false, give a counterexample. a)...

Is each statement true or false? If true, explain why; if false, give a counterexample.

a) A linear system with 5 equations and 4 unknowns is always inconsistent.

b) If the coefficient matrix of a homogeneous system has a column of zeroes, then the system has infinitely many solutions. (Note: a homogeneous system has augmented matrix [A | b] where b = 0.)

c) If the RREF of a homogeneous system has a row of zeroes, then the system has infinitely many solutions.

What happens in b) and c) if we replace “homogeneous” with “non-homogeneous?”

Please explain!

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