DT Q47

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DT Q47

47Four matrices M₁, M₂, M₃ and M₄ of 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 × M₂ ) × (M₃ × M₄ )), the total number of scalar multiplications is pqr + rst + prt. When multiplied as ((M₁ × M₂ ) × M₃ ) × M₄ ), the total number of scalar multiplications is pqr + prs + pst.
If p = 10, q = 100, r = 20, s = 5 and t = 80, then the minimum number of scalar multiplications needed is

Option : C
Explanation :
The problem can be solved using matrix chain multiplication. we get minimum number of multiplication using ((M₁ × M₂ ) × M₃ ) × M₄ )
= 100 × 20 × 5 + 10 × 100 × 5 + 10 × 5 × 80
= 19000.

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