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FinalStand

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## Homework Statement

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.

## Homework Equations

## 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...