Review 8-4

Hajin Ju, 2024062806

Problem 1

What is the dimension of the matrix product AB if A is a p\times q matrix and B is a q\times r matrix?

Solution 1

p\times r

Problem 2

Count the number of scalar multiplications to multiply A and B where A is a p\times q matrix and B is a q\times r matrix.

Solution 2

pqr

Problem 3

Count the number of scalar multiplications where the dimensions of A_1, A_2, and $A_3$$ are 10\times 100, 100\times 5 and 5\times 50, respectively.

(A_1A_2)A_3
A_1(A_2A_3)

Solution 3

5000 + 2500 = 7500
25000 + 50000 = 75000

Problem 4

Fully parenthesize the product A_1A_2A_3A_4. (There are five distinct ways.)

Solution 4

(A_1A_2)(A_3A_4)
(A_1(A_2A_3))A_4
A_1(A_2(A_3A_4))
A_1((A_2A_3)A_4)
((A_1A_2)A_3)A_4

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