4. Split into two subgroups, with m in the first subgroup and n in the second....

 

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4. Split into two subgroups, with m in the first subgroup and n in the second. Everyone choose a (smallish) integer. Produce an m x n matrix A = [a], where a, is the sum of the ith integer from the first subgroup and the jth from the second. +0 Compute A where the column vector has n entries all equal to 1. 5. Let TFF be a linear map, and let À € F. Suppose that T is represented by the mxn matrix A = [au]. From the definition of the linear map XT, show that XT is represented by the matrix AA. 4. Split into two subgroups, with m in the first subgroup and n in the second. Everyone choose a (smallish) integer. Produce an m x n matrix A = [a], where a, is the sum of the ith integer from the first subgroup and the jth from the second. +0 Compute A where the column vector has n entries all equal to 1. 5. Let TFF be a linear map, and let À € F. Suppose that T is represented by the mxn matrix A = [au]. From the definition of the linear map XT, show that XT is represented by the matrix AA.

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