Does the 0 vector not count when determining the dimension?

[brushman]

Homework Statement

If we have ker(T)={0}, why is the dim(ker(T)) = 0?

Does the 0 vector not count when determining the dimension? I thought the answer would be 1.

 

[Dick]

Nope, doesn't count. The zero vector is in any vector space. Even a one-dimensional space has the zero vector in it. The zero vector isn't what makes it one-dimensional.