This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Matrix Multiplication using Recursion”.

1. If Matrix A is of order X*Y and Matrix B is of order M*N, then what is the order of the Matrix A*B given that Y=M?

a) Y*N

b) X*M

c) X*N

d) Y*M

View Answer

Explanation: The Matrix A*B is of order X*N as it is given that Y=M i.e. number of columns in Matrix A is equal to total number of rows in matrix B. So the Matrix A*B must have X number of rows and N number of columns.

2. How many recursive calls are there in Recursive matrix multiplication through Simple Divide and Conquer Method?

a) 2

b) 6

c) 9

d) 8

View Answer

Explanation: For the multiplication two square matrix recursively using Simple Divide and Conquer Method, there are 8 recursive calls performed for high time complexity.

3. What is the time complexity of matrix multiplied recursively by Divide and Conquer Method?

a) O(n)

b) O(n^{2})

c) O(n^{3})

d) O(n!)

View Answer

Explanation: The time complexity of recursive multiplication of two square matrices by the Divide and Conquer method is found to be O(n

^{3}) since there are total of 8 recursive calls.

4. What is the time complexity of matrix multiplied recursively by Strassen’s Method?

a) O(n^{log7})

b) O(n^{2})

c) O(n^{3})

d) O(n!)

View Answer

Explanation The time complexity of recursive multiplication of two square matrices by Strassen’s Method is found to be O(n

^{log7}) since there are total 7 recursive calls.

5. How many recursive calls are there in Recursive matrix multiplication by Strassen’s Method?

a) 5

b) 7

c) 8

d) 4

View Answer

Explanation: For the multiplication two square matrix recursively using Strassen’s Method, there are 7 recursive calls performed for high time complexity.

6. Matrix A is of order 3*4 and Matrix B is of order 4*5. How many elements will be there in a matrix A*B multiplied recursively.

a) 12

b) 15

c) 16

d) 20

View Answer

Explanation: The resultant matrix will be of order 3*5 when multiplied recursively and therefore the matrix will have 3*5=15 elements.

7. If Matrix X is of order A*B and Matrix Y is of order C*D, and B=C then the order of the Matrix X*Y is A*D?

a) True

b) False

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Explanation: Given that B=C, so the two matrix can be recursively multiplied. Therefore, the order of the Matrix X*Y is A*D.

8. What is the time complexity of the fastest known matrix multiplication algorithm?

a) O(n^{log7})

b) O(n^{2.37})

c) O(n^{3})

d) O(n!)

View Answer

Explanation: The Coppersmith-Winograd algorithm multiplies the matrices in O(n

^{2.37}) time. Several improvements have been made in the algorithm since 2010.

9. Is Coppersmith-Winograd algorithm better than Strassen’s algorithm in terms of time complexity?

a) True

b) False

View Answer

Explanation: Since The Coppersmith-Winograd algorithm multiplies the matrices in O(n

^{2.37}) time. The time complexity of recursive multiplication of two square matrices by Strassen’s Method is found to be O(n

^{2.80}). Therefore, Coppersmith-Winograd algorithm better than Strassen’s algorithm in terms of time complexity.

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