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To solve the Matrix Chain Multiplication (MCM) problem numerically, we use dynamic programming to determine the optimal way to parenthesize a given sequence of matrices to minimize the number of scalar multiplications. ### Step 1: Define the Problem Given the matrix dimensions: \[ p = [10, 25, 10, 5, 17] \] This means we have four matrices: \[ A_1: 10 \times 25, \quad A_2: 25 \times 10, \quad A_3: 10 \times 5, \quad A_4: 5 \times 17 \] We need to find the optimal way to fully parenthesize these matrices to minimize the multiplication cost. ### Step 2: Use Dynamic Programming Let \( m[i][j] \) represent the minimum cost ________ _______ ____ ___ _______ _________ _____ ______ _____ ______ _________.
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