Why is the dimension of a kernel with the basis {[0,0,0]} equal to zero What is the dimension of a kernel with the basis {[0,0,0]}?
I'm confused because the definition of the dimension is number of vectors in a basis. So there is 1 vector here which is [0,0,0]. 
Why does my professor say that the dimension of kernel is zero? He mentioned something about the zero vector space.

A basis is defined as a set of linearly independent vectors that span a space. For the row space (kernel) of your problem, it clearly only includes the zero vector. However the zero vector, v, is linearly indepedent (as there exists a scalar, C != 0, such that Cv = 0), therefore the basis of the row space has no dimension.
