Does a homogenous system always have multiple solutions?

[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?

 

[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?

 

[shiri]

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

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.

 

[shiri]

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

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]

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

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]

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?

I guess no. May have no solutions

Am I right?

 

[rock.freak667]

I guess no. May have no solutions

Am I right?

or you can have one solution as well

 

[shiri]

or you can have one solution as well

one solution?

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

why is that? Just curious