# Ax=b1 and Ax=b2 are consistent. Is the system Ax=b1+b2 necessarily consistent?

1. Nov 20, 2012

### iamzzz

1. The problem statement, all variables and given/known data
Suppose A is m*n matrix b1 and b2 are m*1 vector and the systems Ax=b1 and Ax=b2 are consistent. Is the system Ax=b1+b2 necessarily consistent?

2. Relevant equations

3. The attempt at a solution

I think Ax = b1 + b2 should be consistent but i dont know how to prove..

2. Nov 20, 2012

### Dick

No thoughts about how to prove at all? A(x1+x2)=Ax1+Ax2. Think about it some more.

3. Nov 20, 2012

### iamzzz

let x1 be the solution of Ax1=b1 and x2 be the solution of Ax2=b2

So Ax1+Ax2=b1+b2=A(x1+x2)
so (x1+x2)could be x
prove ?
Is this correct ?

4. Nov 20, 2012

### Dick

I would say let x1 be ANY solution to Ax=b. There may be more than one. But why are you asking "Is this correct?". What part of it are you worried about?

5. Nov 20, 2012

### iamzzz

I mean does that prove the problem ?

Anyway thanks for the help

6. Nov 20, 2012

### Dick

I'm just saying I would feel better if you KNEW it solved the problem instead of having to ask. Yes, it's fine.