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## Homework Statement

I am wondering if someone could help me with the following. I am asked to find a 2 by 3 system Ax = b whose complete solution is x = [1 2 0] + w*[1 3 1] Imagine that these are colum matrices because I can't type columns on here.

FIrst, I don't see how you can get a three row matrix if from a 2 by three system? Don't you need a 3 by 3 matrix if your variable is u,v,w since you have three columns?

So, I guess the eventual matrix would looke something like the following:

1 -1 0

0 -3 1

0 0 0

And if the above is A, would be solution be Ax = [1 2 0]?

And then I'm asked to find a 3 by 3 system with these solutions for Ax = b when b = [b1, b2, b3] and b1+b2 = b3? Imagine again that these are column matrices. So would I then get the following matrix:

1 -1 0

3 0 1

0 0 0

so if that is A then I set it to Ax = [1 2 0]. What I did is that I set A from the first part to equal to some b, that satisfies the condition, so say [1 -1 0] and then use matrix addition and substraction to arrive at the new matrix?

Thanks much!