Is the Equation Ax=w Consistent for A in M4,3 and w as v1+v2?

[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

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.

 

[jbunniii]

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?

 

[ykaire]

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]

Well, what is Ax= A(u₁+ u₂)?

 

[ykaire]

Well, what is Ax= A(u₁+ u₂)?

it reduces to x= u₁ + u₂