Question: Problem 3: Let A. .A be the matrices where the dimentions of A, are d-i x d, for i = 1, , n. Here is

Problem 3: Let A. .A be the matrices where the dimentions of A, are d-i x d, for i = 1, , n. Here is a strategy for determining the best orier in which to perform the matrix multiplications to compute A X A2Xx A At each step, choose the largest remaining dimension (from among di.d-), and multiply two adjacent matrices which share that dimension. (a) What is the order of the running time of this algorithm (only to determine the order in which to multiply the matrices, not incuding the actual multiplications)? (b) Either give a convincing argument that this strategy will always minimize the number of mul tiplications, or give an example where it fails to do so

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