As background to this exercise, see Exercise 45. a. If you use Theorem 2.3.4, how many
Chapter 2, Problem 106(choose chapter or problem)
As background to this exercise, see Exercise 45. a. If you use Theorem 2.3.4, how many multiplications of scalars are necessary to multiply two 2 x 2 matrices? b. If you use Theorem 2.3.4, how many multiplications are needed to multiply an n x p and a p x m matrix?In 1969, the German mathematician Volker Strassen surprised the mathematical community by showing that two 2 x 2 matrices can be multiplied with only seven multiplications of numbers. Here is his trick: Suppose you \a bn have to find A B for A = First computeand B =hi = (a + d)(p+s) hi = (c + d)p h 3 = a(q - s) /14 = d(r - p) h 5 = (a + b)s hf> = (c - a)(p+q) hi = (b - d){r + s)ThenAB _ h\ +/14 - h 5 +/17 /13+/15 [ /12 + h4 h 1 + /Z3 - h2 + he
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