Question: (I) Consider the following three functions from R to R. Show that two of them are not linear, and prove that the third is

(I) Consider the following three functions from R to R. Show that two of them are not linear, and prove that

(I) Consider the following three functions from R to R. Show that two of them are not linear, and prove that the third is linear using Lemma 2 T 3y 2y+3z 2y + 3) ())-(-) (())) -(0)-C) = = 5z T2 3x 1 3y Z (II) Prove that T: C C given by T (( ~ )) - ( ) W T3 is not linear. (III) Prove that there does not exist a linear transformation, T: R R, such that ((:)) - () (G)) - (3) (())-(-) T 3 = T = = (+). 2

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