Function for telling if a function is unique and how many solutions it has.

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Hello everyone, I'm a student who's being taught linear algebra, but being assigned matlab homework without any real explanation. I've come across this question and I need assistance with it:
Write an M-file function, that tells whether a system of linear equations has no solution, unique solution, or infinitely many solutions. The code should be such that you enter the coefficient matrix A and the corresponding column vector b. If the number of rows of A is different from the number of entries in b, the output should be an error message and execution stops. Otherwise, the output is a message indicating whether the system has no solution, unique solution, or infinitely many solutions. In this last case, it also tells the number of free variables of the system. In the case of unique solution, the code should also give the solution.
They gave me some p code to 'check what my code should do' as well but I honestly don't know how to use p-code and my version of MATLAB doesn't recognize it.

Accepted Answer

Joel Lynch
Joel Lynch on 9 Jun 2021
Edited: Joel Lynch on 9 Jun 2021
".p" files are purposefully obfuscated, so you cannot copy the code, suggesting your instructor does not want you to use someone else's solution (which probably includes MATLAB Answers). You are meant to use lab4task3 as the "correct" answer that your function should match for the various examples.
If you are looking for advice on a good place to start, I would recommend thinking/reading about what the sizes of A and b (both rows and columns) tell you about whether the system is solvable, underdetermined or overdetermined. That will help you setup switches to alter the function's results to the correct response.
Walter Roberson
Walter Roberson on 10 Jun 2021
The prof is just saying that given a particular A and b matrix, that your own code should produce exactly the same output as lab4task3() produces for those inputs. You do not need to care how the .p is implemented. You should, though, be trying some possible inputs and taking careful note of the format of the outputs or error messages, so that you can produce exactly the same result.
For example if lab4task3(A,b) reports
Wut? Yur b und ur A r incommenserate, know u not?
then you should output exactly the same error message under the circumstances.

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