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Can someone check my answer! Thank you!

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    If a 4x4 matrix A with rows v1, v2, v3 and v4 has determinant detA =-2


    then det (v1, 9v2+5v3, 5v2+8v3, v4) =___?

    2. Relevant equations

    3. The attempt at a solution

    Ok, so I think it should be -18 (since 9 x -2). I mean the determinant should not change when adding columns to each other, however multiplying should have an effect, but I am not quite sure what happened to the v3, like do I multiply the determinant by 8, or 5, or none?
  2. jcsd
  3. Mar 25, 2009 #2


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    I'll give you a sample, det(v1,9*v2+5*v3,v3,v4)=
    9*det(v1,v2,v3,v4)+5*det(v1,v3,v3,v4). What's that? Now what happens if you put the linear combination in for v3 as well?
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