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Homework Help: Prove Ax=w is consistent

  1. Sep 4, 2012 #1
    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. jcsd
  3. Sep 5, 2012 #2


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    Well, can you write [itex]Au_1 + Au_2[/itex] another way?
  4. Sep 5, 2012 #3
    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.
  5. Sep 5, 2012 #4


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    Well, what is Ax= A(u1+ u2)?
  6. Sep 5, 2012 #5
    it reduces to x= u1 + u2
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