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I've been reading through my textbook for some guidance on this, but I have yet to find anything. The question asks to "describe the set of possible solutions when the following occur (assuming Ax=b). I've written my own knowledge in italics - however, I think they require an answer in terms of "no solution"/"# of unique solutions" or "infinite solutions".

(i) detA = 0, b = 0(no inverse)

(ii) detA ≠ 0, b = 0(inverse possible)

(iii) detA = 0, b ≠ 0(no inverse)

(iv) detA ≠ 0, b ≠ 0(inverse possible)

The way I learnt was that if there was 3 solutions, there had to be 3 variables/pieces of information, otherwise it was redundant or inconsistent depending on what you were given. I've yet to learn using determinants and the b-vector.

Any insight would be helpful - Thanks.

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# Homework Help: Square Matrix Scenarios

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