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Linear combo

  1. Sep 26, 2012 #1
    Lets say you have 3 vectors v1, v2,v3. They form a 3x3 matrix.

    Let's say you're asked if v3 is a linear combo of the other two vectors.

    Rref of the matrix gives
    1 0 1
    0 1 0
    0 0 0

    The definition of a Linear combo is v3=c1v1+c2v2 where c1 and c2 are scalars.

    Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?

    Also is 0 a scalar?
     
  2. jcsd
  3. Sep 26, 2012 #2

    jbunniii

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    It IS a linear combination. c2 = 0 is allowed. 0 is a scalar.
     
  4. Sep 26, 2012 #3

    Mark44

    Staff: Mentor

    Assuming this is an augmented matrix, you have c1 = 1 and c2 = 0.
    No, v3 is a linear combination of v1 and v2; namely, v3 = 1v1 + 0v2.
    Yes, unless you're talking about a 0 vector, which in this case would be <0, 0, 0>.
     
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