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Least Square Solution(zeros in one row)

  1. Oct 1, 2009 #1
    1. The problem statement, all variables and given/known data
    Give a least squares solution to Ax=C and give the residual error

    -1, 1, 2;
    1, -1, 0;
    1, -1, 2;


    2. Relevant equations

    Residual Error= |Ax-C|

    3. The attempt at a solution
    I have done an RREF on the Transpose of A times A augmented with the Transpose of A time C and got this:
    1, -1, 0, 2/3;
    0, 0, 1, 1/4;
    0, 0, 0, 0;

    I'm not sure what I should do about the bottom row... I know that SHOULD be always an LSQ but it doesnt seem to come out. I know that bottom row indicates an infinite amount of solutions but not sure how to proceed next. Please help
  2. jcsd
  3. Oct 1, 2009 #2
    Does anyone have any clue????

    If it helps, I tried to set the third variable as a number and first and second as equations in terms of each other (i.e 1st in terms of 2nd).
  4. Oct 2, 2009 #3


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    Homework Helper

    I presume this is a linear algebra class and you've learned about rank and rank deficiency. Is A full rank?
  5. Oct 3, 2009 #4
    not in precise terms...I know the columm space of A is 3x2. I looked up rank in wikipedia...
  6. Oct 4, 2009 #5


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    Homework Helper

    I suggest you look at the 2nd equation. What does that tell you? Then, look at the 1st equation. It may help to write them out.
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