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.
Best Answer
The space spanned by $[0,0,0]$ is $\{[0,0,0]\}$, i.e. then null space.
A basis needs to be made of linearly independant vectors, and thus a family which contains the null vector cannot be a basis !
The basis of the null space would just be the empty set $\emptyset$, hence its dimension is $0$