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Linear Dependence Proof

  1. Jul 30, 2014 #1
    1. The problem statement, all variables and given/known data
    Let x1,x2,x3 be linearly dependent vectors in Rn, let A be a nonsingular n x n matrix, and let y1=Ax1, y2=Ax2, y3=Ax3. Prove that y1, y2,y3 are linearly dependent.




    2. Relevant equations



    3. The attempt at a solution
    My solution was y is equal to the zero vector, thus must be linearly dependent.
     
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  3. Jul 30, 2014 #2

    Orodruin

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    What is y in your solution? You have specified y1, y2, and y3 ...
     
  4. Jul 31, 2014 #3

    HallsofIvy

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    I think you must have misunderstood the problem. y certainly does NOT have to be the 0 vector.
     
  5. Jul 31, 2014 #4

    Fredrik

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    What does the assumption tell you about the vectors ##x_1,x_2,x_3##? The answer to the problem follows almost immediately from the answer to this question.
     
  6. Jul 31, 2014 #5
    Without trying to derail the thread too much, I don't see why ##A## has to be nonsingular.
     
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