Multiple choice

Four matrices M1, M2, M3, and M4 have dimensions p x q, q x r, r x s, and s x t respectively can be multiplied in several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 x M2) x (M3 x M4)) total number of scalar multiplications is pqr + rst + prt.

When multiplied as (((Mi x M2) x M3) x M4) the total number of scalar multiplications is pqr + prs + pst.

If p = 10, q = 100, r = 20, s = 5, and t = 80, then what is the minimum number of scalar multiplications needed ?

  1. 248000

  2. 44000

  3. 19000

  4. 25000
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C Correct answer
Explanation

Multiply as $(M_3 \times M_2 \times M_3) \times M_4$ The total number of scalar multiplication is = qrs + pqs + pst = 10000 + 5000 + 4000 = 19000

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