Question: Find a coefficient matrix A such that the associated linear system Ax = b has (a) Infinitely many solutions for every b, (b) 0 or

Find a coefficient matrix A such that the associated linear system Ax = b has
(a) Infinitely many solutions for every b,
(b) 0 or ∞ solutions, depending on b,
(c) 0 or 1 solution depending on b.
(d) Exactly 1 solution for all b.

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