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  3. 1. (a) consider the following chain of six matrice

1. (a) Consider the following chain of six matrices: A1, A2, A3, A4, A5, and...

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1. (a) Consider the following chain of six matrices: A1, A2, A3, A4, A5, and A6, where Aj is 5 x 10, A2 is 10 x 3, A3 is 3 x 12, A4 is 12 x 5, A5 is 5 x 50, and A6 is 50 6. Find an optimal parenthesization of this matrix-chain. Show both the table containing the optimal number of scalar operations for all slices and the choice table. (b) Prove using the strong form of induction that for any n e N, if n > 1 then a full parenthesization of an n-element expression has n 1 pairs of parentheses. 1. (a) Consider the following chain of six matrices: A1, A2, A3, A4, A5, and A6, where Aj is 5 x 10, A2 is 10 x 3, A3 is 3 x 12, A4 is 12 x 5, A5 is 5 x 50, and A6 is 50 6. Find an optimal parenthesization of this matrix-chain. Show both the table containing the optimal number of scalar operations for all slices and the choice table. (b) Prove using the strong form of induction that for any n e N, if n > 1 then a full parenthesization of an n-element expression has n 1 pairs of parentheses

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