Paper, Order, or Assignment Requirements

1. Suppose you have a chain of 11 matrices, with dimensions given by the
12-tuple, . Thus, has dimensions  and in general,  has dimensions for .  Specifically, the 12-tuple is
(5, 10, 9, 20, 6, 33, 5, 17, 12, 8, 16, 5).  How should you multiply the matrices in this chain so as to minimize the total number of numeric multiplications? Give your answer both as a parenthesization of the chain of matrices and also as the 10 specific matrix multiplications in order that produce this minimal number. (For example, if you were to multiply  times followed by a multiplication on the right by  , you could indicate these steps in order as:

(1) Compute
(2) Compute

And so forth (I am not claiming that these steps would necessarily occur.)  Important: Show your work!

1. The first stanza of King Lear’s famous Act III scene 2 speech, with all of the punctuation and spaces removed and all lower case (from First Folio, 1623 edition, with original spelling) is: