Question: Let Bk = { l, . .. , k} be the standard k-element set. Ftecall that the matrix MU) associated to a map f :

Let Bk = { l, . .. , k} be the standard k-element set. Ftecall that the matrix MU") associated to a map f : Em > B\" is the arrayr with a rows and m columns a\" IE112 \"1m IE321 H22 \"2: M(f} = 1Jill 1.12 '" llamt-1 where a\" = 1 preciser when fi) = r' and fj = [1 otherwise. (Side remark: we may think of MU\") as a list of binary values {cu} indexed by B\" x 3,", or more precisely, as a map E" x Em > {[1, 1}.) 1. Let f : B; > B4 be the map dened by f(x} = 2;ir.2 + T3: 2. Compute M(f}. 2. It r : 33 ) .33 is a permutation of the domain. and I : B4 > R; is a permutation of the codomain, then we may change the map f into the following map f' = I o f n r : B3 :r B4. EaJ Without permuting the codomain, is it possible to choose r so that the matrix of f' is equal to 1 D 1 D i] {ll 1 i] {i D It so, how? 2b] (in the other hand, if we keep the domain fixed and permute the codomain, is it possible to obtain the matrix above for f\"? If so, how

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