Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 6 / c / iii

No. The nonzero vector $v=(2,-9,-3,21{)}^{\top }$ is in the kernel of the linear map, so $T(v)=T(0)=0$ although $v\ne 0$. A linear map is injective exactly when its kernel consists only of zero.