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Linear algebra conceptual question

  1. Jan 19, 2013 #1
    1. The problem statement, all variables and given/known data

    Let A be a 5x3 matrix. If

    b=a1+a2=a2+a3

    then what can you conclude about the number of solutions of the linear system Ax=b? Explain

    I don't have the solution for this problem, and my first thinking was the system would be overdertermined, and be most likely inconsistent. However i'm not 100% if i am even approaching the problem correctly

    Thanks


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 19, 2013 #2

    Ray Vickson

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    What are ##a_1, a_3, a_3##? Rows of A? Columns of A? Something else?
     
  4. Jan 19, 2013 #3
    rows of a
     
  5. Jan 19, 2013 #4

    vela

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    The rows of A have 3 elements each while b has 5 elements. How can ##a_1+a_2=b## possibly hold?
     
  6. Jan 19, 2013 #5
    Don't really understand
     
  7. Jan 19, 2013 #6

    vela

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    Look at the dimensions of A, x, and b. A is 5x3, so what do the dimensions of x and b have to be?
     
  8. Jan 20, 2013 #7
    it would have to be 5x1?
     
  9. Jan 20, 2013 #8

    vela

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    Right. Now if ##a_1## and ##a_2## represent rows of A, how many elements does each have? Can ##a_1+a_2## equal ##b##?
     
  10. Jan 20, 2013 #9
    5 elements in order to equal b.

    and no a1+a2 alone can not equal b. it must be coupled with 4 other rows of a1+a2. I hope I interpreted that correctly.
     
  11. Jan 20, 2013 #10

    SammyS

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    I suspect that a1, a2, and a3 are the columns of matrix A .
     
  12. Jan 20, 2013 #11
    I think you're correct sammy I just reread the question.
     
  13. Jan 20, 2013 #12

    SammyS

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    Can you get a solution now ?
     
  14. Jan 20, 2013 #13
    Sorry but i'm still confused, I am having a hard time transitioning to this deeper thinking math course.

    But I think the answer would be that a 5x3 matrix should have an answer in the 5x1 form

    So b would be could be an infinite array of 5x1 different matrices.
     
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