Question

Find the dimensions of the following subspace of R4.
a) all voctors of the form (0,a,b,c).

Answer 1

dimension = number of vectors in a basis set

heard of `basis` before ?

Answer 2

in 3-D
if you had points (0,a,b), they would like in a plane (y-z plane), which has 2 dimensions
(i.e. 1 less than 3-D)
by analogy you can answer your question.