Which of the following subsets of $R^3$ are actually subspaces?
(a) The plane of vectors $(b_1 , b_2 , b_3)$ with $b_1 = b_2$
(b) The plane of vectors with $b_1 = 1$.
(c) The vectors with $b_1b_2b_3 = 0$.
Is my answer for (a) correct and I don't understand what (b) and (c) mean?
(a) this is a subspace because if you have three vectors in $R^3$ and two of them are equal that means you have a plane in $R^3$ and that is closed under addition and subtraction.