[10 points) The matriz chain multiplication problem finds the minimum number of multi- plications needed to calculate the product of a series of matrices. For example, for three matrices with dimensions Al : 2 x 3, A2 : 3 x 2, A3 : 2 x 4, then (A1 A2) A3 results in 2 x 3 x 2 + 2 x 2 x 4 = 28 multiplications, A1 (A2 A3) results in 3 x 2 x 4+2 x 3 x 4 = 48 multiplications, and thus the former is better. Consider 5 matrices of the following dimensions A : 6 x 5; A2 : 5 x 7; A3 : 7 x 10; A4 : 10 x 2; A5 : 2 x 8. Here, we define a subproblem C[i, j] to be the minimum number of multiplications for the product of A; Ai+1 Aj. Fill the following table for C to find out the minimum number of multiplications for the product of A1 A2 Az A4 45 A6 A7. For each value you fill into the table, you need to exhibit the specific calculations that you do to get that value. 1 2 3 4 5 ili 0 1 0 2 3 0 0 4 5 0