Question

question:
there are two systems of MXN non homogeneus equations:
they both are from Ax=b type
and their redused A is the same.

the first system c' has infinit number of solution
does the other one(c) has infinit number of solutions too .

?

i know that its wrong but in this course i have a list of laws regarding systems of equations
and if the answer was "yes" then i should have prove it.

but i dont know why by the laws its impossible???(so i need to look for contradicting example)

Answer 1

I don't know what you mean by 'reduced A', but if the linear functions functions are the same, the solutions of the two equations only differ by a constant vector and thus there are equally many solutions for both.