# Thread: Solutions of Linear Systems I

1. ## Solutions of Linear Systems I

Write a short paragraph to answer each of the following questions about solutions of systems of linear equations. You should not perform any calculations, but instead base your explanations on the appropriate properties.

[1] One solution of the homogeneous linear system
x + 2y + z + 3w = 0
x - y + + w = 0
y - z + 2w = 0
is x=-2, y=-1, z=1, ans w=1. Explain why x=4, y=2, z=-2, and w=-2 must also be a solution. Do not perform any row operations.

[2] The vectors x1 and x2 are solutions of the homogeneous linear system Ax=0. Explain why the vector 2x1-3x2 must also be a solution.

2. You need to tell us what you've tried already, and where you're confused. This looks a lot like homework or an exam, and we're not going to (not supposed to, at least) just write the answers for you.

3. It's homework. I tried to approve some of them but using calculations. Now, I need hints on how to approve them using theorems. I'm going to post what I worked through the weekend.

Appreciate any help.

4. one thing you can do which will probably be somewhat better received, is to list which theorems you are allowed to use, and what you think they imply, and how they might apply to this problem. the point of these problems is not to test your skill at calculation, but rather, how you can use the theorems to get results with a minimum of calculation.

these two problems are not that difficult, they are basic applications of general principles of linear algebra.