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 a1a2a3a4 using the basic matrix multiplication method is

Answer 1

Answer:

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Answer 2

The minimum number of scalar multiplications required to find the product a1a2a3a4 using the basic matrix multiplication method is 3500.

Step-by-step explanation:

Given,

Dimension of a1 = 10 x 5

Dimension of a2 = 5 x 20

Dimension of a3 = 20 x 10

Dimension of a4 = 10 x 5

For a given matrix A of dimension (p x q) and matrix B of dimension (qxr),

The minimum number of scalar multiplications required to find the                                   product AB = p x q x r

and the dimension of the product AB = p x r

So,

for product a1a2 ,

minimum number of scalar multiplications required  = 10 x 5 x 20 = 1000

and dimension of a1a2 = 10 x 20

Now,

for product a1a2a3,

minimum number of scalar multiplications required  = 10 x 20 x 10 = 2000

and dimension of a1a2a3 = 10 x 10

Now,

for product a1a2a3a4 ,

minimum number of scalar multiplications required  = 10 x 10 x 5 = 500

and dimension of a1a2a3a4 = 10 x 5

⇒ Total no.  of scalar multiplications required  = 1000 + 2000 + 500 = 3500

So,

The minimum number of scalar multiplications required to find the product a1a2a3a4 using the basic matrix multiplication method is = 3500

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