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Clarence

  • one year ago

Absolutely stumped on this one (all matrices 4x1): The system of equations Ax = c has solutions x = (-4, 4, -3, -2) + p(2, 1, -3, -4) + q(2, -3, 3, -4). The solution set of the system Ax = 0 consists of all vectors x = ?

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  1. ganeshie8
    • one year ago
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    Hey

  2. anonymous
    • one year ago
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    @ganeshie8 hi he or she ask me to help lol just playin

  3. clarence
    • one year ago
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    I'm thinking that it could be x = p(2, 1, -3, -4) but I could be way wrong..

  4. ganeshie8
    • one year ago
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    good thinking, remember that the complete solution for \(Ax=c\) is given by a particular solution and the complete nullspace : \[\large {X_{\text{complete}} ~~= ~~X_{\text{particular}} + X_{\text{null}}}\]

  5. ganeshie8
    • one year ago
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    In the present problem \[\large X_{\text{complete}} = (-4, 4, -3, -2) + \color{red}{p(2, 1, -3, -4) + q(2, -3, 3, -4)}\]

  6. ganeshie8
    • one year ago
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    that entire red part constitutes the nullspace that is, the solutions to the system \(Ax=0\)

  7. anonymous
    • one year ago
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    @ganeshie8 lol don't be blowing up my notification k

  8. clarence
    • one year ago
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    Oh right, that makes sense! I think I might've forgotten about the Xcomplete = Xparticular + Xnull when my lecturer was explaining about it, thanks a lot, really appreciate the help!

  9. ganeshie8
    • one year ago
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    np :) here is a little challenge : try finding the matrix \(A\) from the given solutions

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