Prove jacobian matrix is identity of matrix of order 3

  1. If f(x,y,z) = xi + yj +zk, prove that Jacobian matrix Df(x,y,z) is the identity matrix of order 3.

    Because the D operator is linear, D1f(x,y,z) = i, D2f(x,y,z) = k, D3f(x,y,z) = k

    There is clearly a relationship between this and some sort of identity, but I'm not sure how to state it, and I don't understand the order of linear transformations. Could someone help me?
     
  2. jcsd
  3. *typo on D2f(x,y,z) = j

    actually I was just rethinking about the problem. could Df(x,y,z) = ((1,0,0),(0,1,0),(0,0,1)), which becomes an identity matrix, and the order of 3 refers to 3x3 matrix?
     
  4. Dick

    Dick 25,824
    Science Advisor
    Homework Helper

    Yes, exactly.
     
  5. awesome. thanks!
     
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