Like is [1,0] one dimensional or is [1,1]?
I assume you mean x and y to represent the components of a vector is . Yes, the set of vectors [x, y] with y= x, that is all vectors of the form [x, x], is a subspace of dimension 1. The set of all vectors of the form [x, 0] and the set of all vectors of the form [0, y] are also subspaces of dimension 1. In fact, the set of all vectors of the form [x, mx], for m any fixed number, is a subspace of dimension 1.Is the dimension of a subspace in R2 1 when x=y or when x or y is zero?
I have no idea what you mean by this. A single non-zero vector is not a subspace at all and has no "dimension". Of course, [1, 0] is in the subspace of all vectors of the form [x, 0] and [1, 1] is in the subspace of all vectors of the form [x, x].Like is [1,0] one dimensional or is [1,1]?