Question: (20 pts) Let A,..., A6 be matrices with dimension 5 10, 10 3,3 12, 12 5,5 50, 50 6, respectively. Let Cij be the

(20 pts) Let A,..., A6 be matrices with dimension 5 10, 10

(20 pts) Let A,..., A6 be matrices with dimension 5 10, 10 3,3 12, 12 5,5 50, 50 6, respectively. Let Cij be the smallest number of scalar multiplications needed for computing the matrix product A, A+11 Aj, assuming that multiplying an rxs matrix and an s xt matrix takes rst scalar multiplications. Consider the algorithm we discussed in class. Mark by T(=True) or F(=False) each of the following statements: (1) (5 pts) C1,5 = 1655. (2) (5 pts) C2,6 is computed before C1,3. (3) (5 pts) C2,5 is derived from C2,3 and C4,5. (4) (5 pts) The optimal order to multiply A, tiplications is ((A1A2) ((A3 (A4A5)) A6)) A6 with fewest number of scalar mul-

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