# Prove Ax=w is consistent

1. Sep 4, 2012

### ykaire

1. Let A∈ Μ4,3
(that is, a 4 x 3 matrix). Let v1, v2 ∈ R^4 and let w = v1 +v2. Suppose there exists u1, u2 as an element of R^3 such that v1 = Au1 and v2= Au2
prove the Ax=w is consistent

2. Relevant equations

3.i honestly don't know if i'm doing this correctly at all, but this is what I have done so far:
Ax=w where A is a 4x3 matrix.
Ax=v1 + v2
Ax=Au1 + Au2
then i don't know what to do.

Last edited: Sep 5, 2012
2. Sep 5, 2012

### jbunniii

Well, can you write $Au_1 + Au_2$ another way?

3. Sep 5, 2012

### ykaire

I guess I could write the equation as

x= u1 + u2

but, like i said, i don't even know if i even started the problem off correctly.

4. Sep 5, 2012

### HallsofIvy

Staff Emeritus
Well, what is Ax= A(u1+ u2)?

5. Sep 5, 2012

### ykaire

it reduces to x= u1 + u2