Compute the optimal number of scalar multiplications required to
multiply the following matrices.
A1 of order 30 X 35 ; A2 of order 35 X 15 ; A3 of order 15 X 5
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We have many ways to do matrix chain multiplication because matrix multiplication is associative. In other words, no matter how we parenthesize the product, the result of the matrix chain multiplication obtained will remain the same. Here we have four matrices A1, A2, A3, and A4, we would have:
((A1A2)A3)A4 = ((A1(A2A3))A4) = (A1A2)(A3A4) = A1((A2A3)A4) = A1(A2(A3A4)).
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