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Linear Algebra: linear equations

  1. Sep 14, 2009 #1
    Show that if u and v are solutions of the linear system Ax = b, then w = 1/4 u + 3/4 v is also a solution of Ax = b.
     
  2. jcsd
  3. Sep 14, 2009 #2
    Just plug it in and use the fact that matrix multiplication is linear.
     
  4. Sep 14, 2009 #3
    Plug what? where?

    Ax=b, then b=uv ? and uv=w? uv = 1/4u + 3/4v?
     
  5. Sep 14, 2009 #4

    HallsofIvy

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    You want to show that w "is also a solution of Ax= b".

    So "plug" w in for x: Aw= what? Use the fact that w= (1/4)u+ (3/4)v and that A is a linear transformation.
     
  6. Sep 14, 2009 #5

    tiny-tim

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    Amy-Lee, forget x …

    you know that Au = b and Av = b,

    so just carry on from there. :wink:
     
  7. Sep 15, 2009 #6
    thanks TT, I will try that
     
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