(1) For each of the following subsets of R^3, prove that it is a subspace or prove that it is not a subspace.
https://imgur.com/a/WIfqmDj
Did I get it right?
I'm especially concerned with the first part, I don't think I did that right..
(1) For each of the following subsets of R^3, prove that it is a subspace or prove that it is not a subspace.
https://imgur.com/a/WIfqmDj
Did I get it right?
I'm especially concerned with the first part, I don't think I did that right..
Yes. I would phrase it something like this: $L = \{[a,b,c]|a=0\}$ To see that $[a,b,c]=[0,0,0]\in L$ just note that $a=0$.
(I have used rows instead of columns to save typing. The idea is the same.)
The set of vectors, [a, b, c] with the condition that a= 0 is just the set of all [0, b, c] where b and c can be any numbers. In particular, b and c can be 0 which gives the zero vector, [0, 0, 0].