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Do i have right answer? Linear independence

  • 27-11-2009 3:46pm
    #1
    kennyrsb
    Closed Accounts Posts: 178 ✭✭


    Determine whether or not the set V is linearly independent over R

    v= { v1= [1] , v2= [2] , v3= [2] }
    ............[1]...........[3].........[2]
    ............[-1]........[1]..........[2]

    3 equations derived:

    1) C1+2C2+2C3=0
    2) C1+3C2+2C3=0
    3) -C1+C2+2C3=0

    Am i on the right track here, i figure that you get 2C3=C1-C2 from 3), sub that in to 2) and get C1=-C2 which when put in to 1) gives C2=0

    bit mixed up to be honest, not sure weather this shows linear independence or not
    :confused:


Comments

  • #2
    Fringe
    Registered Users, Registered Users 2 Posts: 1,082 ✭✭✭Fringe


    The easiest way is to write the equations you've derived as a system of linear equations. Then find the determinant. If it's nonzero, it means the matrix is invertible so the only solution is the trivial solution and this means it's linearly independent. If it is zero, it is dependent.


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