Question

Let A₁, A₂, A₃, and A₄ be four matrices of dimensions 10 x 5, 5 x 20, 20 x 10, and 10 x 5, respectively. The minimum number of scalar multiplications required to find the product A₁ A₂ A₃ A₄ using the basic matrix multiplication method is ______.

Answer 1

Correct answer is 1500

No. of ways of multiplying the chain of matrices = 2^m C_m/m+1

Where m= no. of multiplications (not matrices)

⇒ ⁶C₃/3+1 = 5