Suppose we know that a linear system Ax = b has a unique solution. What can we say about the solutions of the linear system Ax = 0?
a) It has the same solution.
b) The solution to Ax = b is also a solution to Ax=0, but there may be other solutions.
c) Ax = 0 has a unique solution, but it may be different from the solution to Ax = b.
d) The solution to Ax = b is also a solution to Ax = 0, but the latter has one more solution, namely x= 0.
e) Ax=0 has infinitely many solutions, but the solution to Ax=b need not be one of them.
f) none of the above.
The Attempt at a Solution
I kinda understand the problem, but not sure what the multiple choice options meant.
For now I think the correct option is option B. I don't understand what is the difference between this option (b) and option (d), what is x=0? Does it mean a system of 0x+0y+... and etc? If so then this is false since it has more than just this it could have ifinitely many solutions not just 0x+0y...? I am confusing myself I think...