Engineering Questions with Answers - Multiple Choice Questions

# Matrix Multiplication using Recursion MCQ’s

1 - Question

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

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 - Question

How many recursive calls are there in Recursive matrix multiplication through Simple Divide and Conquer Method?
a) 2
b) 6
c) 9
d) 8

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 - Question

What is the time complexity of matrix multiplied recursively by Divide and Conquer Method?
a) O(n)
b) O(n2)
c) O(n3)
d) O(n!)

Explanation: The time complexity of recursive multiplication of two square matrices by the Divide and Conquer method is found to be O(n3) since there are total of 8 recursive calls.

4 - Question

What is the time complexity of matrix multiplied recursively by Strassen’s Method?
a) O(nlog7)
b) O(n2)
c) O(n3)
d) O(n!)

Explanation: The time complexity of recursive multiplication of two square matrices by Strassen’s Method is found to be O(nlog7) since there are total 7 recursive calls.

5 - Question

How many recursive calls are there in Recursive matrix multiplication by Strassen’s Method?
a) 5
b) 7
c) 8
d) 4

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

6 - Question

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

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

7 - Question

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

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 - Question

What is the time complexity of the fastest known matrix multiplication algorithm?
a) O(nlog7)
b) O(n2.37)
c) O(n3)
d) O(n!)

Explanation: The Coppersmith-Winograd algorithm multiplies the matrices in O(n2.37) time. Several improvements have been made in the algorithm since 2010.

9 - Question

Is Coppersmith-Winograd algorithm better than Strassen’s algorithm in terms of time complexity?
a) True
b) False