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Four  matrices  M1, M2, M3 and M4 of dimensions p×q, q×r, r×s and s×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:

Four  matrices  M1, M2, M3 and M4 of dimensions p×q, q×r, r×s and s×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: Correct Answer <p>19000</p>

Multiply as ((M1×M2)×M3))×M4

The total number of scalar multiplication is
= qrs pqs pst
= 10000+5000+4000 = 19000

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