The <rank-nullity theorem> states $\dim V=\dim\ker T+\dim\operatorname{im}T$ for a <linear map> from a finite-dimensional <vector space> $V$. Here the domain has dimension four and the <image> has dimension two. Thus \b[$\dim\ker T=4-2=2$]. For example, a <kernel> <basis> is $\{(-2,-1,1,0),(-1,-2,0,1)\}$, as follows from the reduced equations.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Digital systems, linear algebra, introduction to formal proof / 5 / c / ii / Solution

 Solution (source code)