Clarence
  • Clarence
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 = ?
Mathematics
chestercat
  • chestercat
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ganeshie8
  • ganeshie8
Hey
anonymous
  • anonymous
@ganeshie8 hi he or she ask me to help lol just playin
Clarence
  • Clarence
I'm thinking that it could be x = p(2, 1, -3, -4) but I could be way wrong..

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ganeshie8
  • ganeshie8
good thinking, remember that the complete solution for \(Ax=c\) is given by a particular solution and the complete nullspace : \[\large {X_{\text{complete}} ~~= ~~X_{\text{particular}} + X_{\text{null}}}\]
ganeshie8
  • ganeshie8
In the present problem \[\large X_{\text{complete}} = (-4, 4, -3, -2) + \color{red}{p(2, 1, -3, -4) + q(2, -3, 3, -4)}\]
ganeshie8
  • ganeshie8
that entire red part constitutes the nullspace that is, the solutions to the system \(Ax=0\)
anonymous
  • anonymous
@ganeshie8 lol don't be blowing up my notification k
Clarence
  • Clarence
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!
ganeshie8
  • ganeshie8
np :) here is a little challenge : try finding the matrix \(A\) from the given solutions

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