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Given a matrix A, the equation Ax=b might have 0 solutions for all b, or 1...

Given a matrix A, the equation Ax=b might have 0 solutions for all b, or 1 solution for all b, or 0 solutions for some choices of b and 1 solution for others, or 0 solutions for

some choices of b and ∞ solutions for others, or 1 solution for some b and ∞ solutions for others, or 0,1, or ∞ solutions for different choices of b. (7 different combinations in

all.) Which of these combinations are actually possible? Justify your answer

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The solution is based on the following criterion

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