Question: 2 3 4) Let A be the following matrix: 4 5 (i) Compute A T . A 6 7 (ii) Now, for a general matrix

2 3 4) Let A be the following matrix: 4 5

2 3 4) Let A be the following matrix: 4 5 (i) Compute A T . A 6 7 (ii) Now, for a general matrix A, (not a specific example do not use specific entries and do not choose a specific size) prove that the entry in the ih row and ith column of AA" must be the sum of the squares of the i" row of A. T th T (iii) Prove that for a general matrix A, the trace of the product AA is the , " sum of the squares of the entries of A

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