(4) Use Strassens algorithm to compute the following matrix product. Show your work: 1 3 7 5 6 8 4 2

(5) Show how to multiply the complex numbers a + bi and c + di using only three multiplications of real numbers. Recall that (a+bi)(c+di) = (acbd) +i(ad+bc). Hint: generate the real part and the imaginary part separately.

(6) Write up a proof using Guess and Check (as we discussed in class) that Strassens algorithm runs in the asymptotic time that is claimed.

(4) Use Strassen's algorithm to compute the following matrix product. Show your work: (1 3 6 8 17 5 4 2) (5) Show how to multiply the complex numbers a + bi and c+ di using only three multiplications of real numbers. Recall that (a+bi)(c+di) = (ac-bd)+i(ad+bc). Hint: generate the real part and the imaginary part separately. (6) Write up a proof using Guess and Check (as we discussed in class) that Strassen's algorithm runs in the asymptotic time that is claimed