Question: (5) For two linear transformations S, 7 : R R, their sum S + T is defined as in caleulus: (S + 1)) = 8S(x)

(5) For two linear transformations S, 7" : R R, their sum S + T is defined as in caleulus: (S + 1)) = 8S(x) +1T(x). Taking = },. .., ,, we see that the matrix of + T is the entrywise sum of those of S, 7T". (a) Verify, without using matrices, that for linear transformations 7' : R R and 51,5 : R 5 R*, we have (S + S3) 0T =Sj0T 4+ S30T

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