Thread: Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

1. Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

I already posted one of these proofs, but I figured I would combine the rest into an album and submit them at once.

The questions is to prove if the given subsets are a subspace of R^3.

I'm confident that I did a and b well enough. For c, I did not know how to handle the inequality, so I did what I thought was best. I am also worried because it says to prove or disprove, and all mine are proofs..

I would appreciate any feed back on my proofs.

https://imgur.com/a/LYHEptt

2. Re: Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

Originally Posted by MrJank
For c, I did not know how to handle the inequality, so I did what I thought was best. I am also worried because it says to prove or disprove, and all mine are proofs..
For 1c)
$\vec a = {\left\langle {1,2,3} \right\rangle ^T}~\&~\vec b = {\left\langle { - 2,4,3} \right\rangle ^T}\text{ then }~\vec a + ( - 1)\vec b = ?$

3. Re: Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

Originally Posted by Plato
For 1c)
$\vec a = {\left\langle {1,2,3} \right\rangle ^T}~\&~\vec b = {\left\langle { - 2,4,3} \right\rangle ^T}\text{ then }~\vec a + ( - 1)\vec b = ?$
a would be greater than c, violating the rules of the subspace? That would mean it is not closed under addition?