# Prove Ax=w is consistent

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

## Homework 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:

jbunniii
Homework Helper
Gold Member
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

## Homework 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.

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

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

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.

HallsofIvy