Homogenous system

1. Sep 27, 2009

shiri

If a homogenous system Ax = 0 has infinitely many solutions, then for a non-zero vector b, the associated system Ax = b ____ have _______

In my assignment, the answer I wrote on this question is must have many solutions. However, what I got is wrong.

Can anybody tell me why it is wrong?

Last edited: Sep 27, 2009
2. Sep 27, 2009

rock.freak667

If Ax=0 gives infinite solutions and Ax=b => Ax≠ 0, why do you think it would give the same infinite number of solutions?

3. Sep 27, 2009

shiri

Well I am assuming there has to be many solutions since Ax=0 gives infinite solutions.

Plus, no solution or/and one solution sounds less appropriate than many solutions at the moment I answer the question.

4. Sep 27, 2009

shiri

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

5. Sep 27, 2009

rock.freak667

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?

6. Sep 27, 2009

shiri

I guess no. May have no solutions

Am I right?

7. Sep 27, 2009

rock.freak667

or you can have one solution as well

8. Sep 27, 2009

shiri

one solution?

So it's C? must have either one solution or no solution?

why is that? Just curious