The discussion revolves around the properties of homogeneous systems of equations, specifically the implications of having infinitely many solutions for the system Ax = 0 and how that relates to the system Ax = b for a non-zero vector b.
The discussion is active, with participants expressing differing views on the implications of the properties of homogeneous systems. Some participants are seeking clarification on the reasoning behind their assumptions, while others are questioning the validity of their conclusions regarding the number of solutions for Ax = b.
Participants are working within the constraints of a homework assignment and are referencing specific choices provided by a teacher regarding the nature of solutions for the system Ax = b.
rock.freak667 said:If Ax=0 gives infinite solutions and Ax=b => Ax≠ 0, why do you think it would give the same infinite number of solutions?
rock.freak667 said:If Ax=0 gives infinite solutions and Ax=b => Ax≠ 0, why do you think it would give the same infinite number of solutions?
shiri said:Teacher gave me these choices:
A. may have exactly one solution
B. must have many solutions
C. must have either one solution or no solution
D. may have no solution
E. need not satisfy any of the above
rock.freak667 said:For a system of equations written in the form Ax=b, you can have one solution, no solutions or infinite solutions.
You know for Ax=0 you have infinite solutions.
So for Ax≠ 0 would you still have infinite solutions?
shiri said:I guess no. May have no solutions
Am I right?
rock.freak667 said:or you can have one solution as well