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Prove Ax=w is consistent

  • Thread starter ykaire
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  • #1
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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:

Answers and Replies

  • #2
jbunniii
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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 [itex]Au_1 + Au_2[/itex] another way?
 
  • #3
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Well, can you write [itex]Au_1 + Au_2[/itex] 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.
 
  • #4
HallsofIvy
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Well, what is Ax= A(u1+ u2)?
 
  • #5
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Well, what is Ax= A(u1+ u2)?
it reduces to x= u1 + u2
 

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