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To find the optimal way of multiplying a sequence of matrices using Matrix Chain Multiplication, we use Dynamic Programming to minimize the total number of scalar multiplications. --- ### Step 1: Dimensions Array We define the dimension array `p[]` from the matrix sizes. Given: * A₁ = 10×15 * A₂ = 15×5 * A₃ = 5×20 * A₄ = 20×10 So, the dimensions array becomes: ``` p = [10, 15, 5, 20, 10] ``` This means: * A₁ is 10×15 → p\[0]×p\[1] * A₂ is 15×5 → p\[1]×p\[2] * A₃ is 5×20 → p\[2]×p\[3] * A₄ is 20×10 → p\[3]×p\[4] --- ### Step 2: Create m and s Tables We create two tables: * `m[i][j]`: Minimum number of scalar multiplications needed to compute Ai..Aj. * `s[i][j]`: Index at which the ______ __________ ____ ________ ______ _________ ______ ______ _______ _____ ______ _____.
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