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Are the following functions linear? If so, find its matrix. If not, give a counterexample. (a) The addition operation $+:R_{2}?R$. (b) The multiplication operation $?:R_{2}?R$. (c) The coordinate swap $T:R_{2}?R_{2}$, where $T(x,y)=(y,x)$. (d) The averaging operation $T:R_{n}?R$, taking a list of $n$ numbers to their average (arithmetic mean). (e) The minimum operation $min:R_{n}?R$.

(a) The linear function R2->R2 is represented by the addition operation +. The identity matrix, indicate