## 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 = ?

1. ganeshie8

Hey

2. anonymous

@ganeshie8 hi he or she ask me to help lol just playin

3. clarence

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

4. ganeshie8

good thinking, remember that the complete solution for $$Ax=c$$ is given by a particular solution and the complete nullspace : $\large {X_{\text{complete}} ~~= ~~X_{\text{particular}} + X_{\text{null}}}$

5. ganeshie8

In the present problem $\large X_{\text{complete}} = (-4, 4, -3, -2) + \color{red}{p(2, 1, -3, -4) + q(2, -3, 3, -4)}$

6. ganeshie8

that entire red part constitutes the nullspace that is, the solutions to the system $$Ax=0$$

7. anonymous

@ganeshie8 lol don't be blowing up my notification k

8. 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!

9. ganeshie8

np :) here is a little challenge : try finding the matrix $$A$$ from the given solutions