Key property General question:We have matrices A1,...An,we want to find the best order for A1×…×An o Dimension of Ai:mi-1x mi ■ One way to find the optimum:Consider the last step. Suppose:(A1×…×Ai)×(Ai+1×…×An)for s0mei∈{1，.，n-1}. cost(1,n)=cost(1,i)+cost(i+1,n)+ momimn 6Key property ◼ General question: We have matrices 𝐴1, …, 𝐴𝑛, we want to find the best order for 𝐴1 × ⋯ × 𝐴𝑛 ❑ Dimension of 𝐴𝑖 : 𝑚𝑖−1 × 𝑚𝑖 ◼ One way to find the optimum: Consider the last step. ❑ Suppose: 𝐴1 × ⋯ × 𝐴𝑖 × 𝐴𝑖+1 × ⋯ × 𝐴𝑛 for some 𝑖 ∈ 1,… , 𝑛 − 1 . ◼ cost 1, 𝑛 = cost 1, 𝑖 + cost 𝑖 + 1, 𝑛 + 𝑚0𝑚𝑖𝑚𝑛 6