Null space

[Ansh malhotra]

I have problem in getting this topic. Please clarify certain doubts.
1) is dimension of matrix equal to rank plus null space.

IN simplest terms what is a null space of a matrix example if Any

[knowpraveen]

This could be easily explained in the context of vectors. It's all the same in practice. The set of vectors which give 0 upon undergoing a transformation in say T, where T is the linear mapping. Look at this in the context of matrices to get the idea. Remember, a vector could be represented in the form of a matrix. I'm not sure what you meant with the first doubt, it doesn't look consistent with the idea of vectors or matrices for that matter. Null matrix + rank makes no sense at all. Infact, for a vector dim V=dim null T + dim range T since this is just enough to span the entire vector space V in any case. Here, dim is the dimension of the basis of the corresponding vectors.