Past exam of the mathematics course of the University of Oxford / 2021 / Prelims / Mathematics I / 2 / a / i / Solution

The rank-nullity theorem for a linear map $T:V\to W$, with $V$ a finite-dimensional vector space over a field $F$, isHere the nullity is the dimension of the kernel of a linear map, and the rank of a linear map is the dimension of its image of a linear map.