- #1
ivanyo
- 5
- 0
Hi everyone,
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 learned 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.
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 learned 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.