{c}

If $TS=\operatorname{id}_W$, every $w\in W$ would satisfy $w=T(Sw)$, so $T$ would be a <surjective linear map>. But its <image of a linear map> has <dimension> at most $\dim V=2$, whereas $\dim W=3$. Therefore \b[no such $S$ exists]. This is the obstruction to a <right inverse>: $T$ cannot reach every target <vector>.

Solution

Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics I / 1 / c / ii / Solution

 Solution (source code)