Answered: Q1. Design a generic matrix multiplier.…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Q1. Design a generic matrix multiplier. Here ‘generic’ means the design should work for any
matrix multiplication X∙Y = Z, where the matrices X, Y, and Z are of sizes a×b, b×c, and a×c
respectively. Now, pick a, b, c from the last three digits of your roll number. ( If any of the digits
is 0, take 3 instead of it; if two digits are 0s, then take 3 for the first 0, and 5 for the second 0)
For Example, if the last three digits are 123 then a = 1, b = 2, and c = 3; if the last three digits
are 204 then a = 2, b = 3, c = 4; f the last three digits are 100 then a = 1, b = 3, c = 5.

Expert Solution

Step 1

NOTE: Implementation provided in c++ language.

Considerations are made as specified in the question:

While implementing the program, the last three digits of the roll number are taken as input from the user.
- If any digit in the number is '0' then that digit is replaced with '3'.
- If any two digits in the number are '0' then the first digit is replaced with '3' and the second digit is replaced with '5'.
Three digits of roll numbers are used as sizes of the matrix.
- The first digit of the roll number is 'a'.
- The second digit is 'b'.
- The third digit is 'c'.
Matrix X with size a*b, Matrix Y with size b*c
- ex: a=1 b=2 c=3
- Data in matrix X with size 1*2,rows =1, columns=2

- Data in matrix Y with size 2*3, rows=2 columns =3

- multiplication of matrix X and Y:

The matrix Z of size 1*3 is generated. Matrix Z size is a*c

Step-2

CODE:

#include <iostream>

using namespace std;

int main()

{

int rollnumber;

int a, b, c;

int X[10][10], Y[10][10], Z[10][10], i, j, k;

cout << "Enter last three digits of rollnumber:" << ends;

cin >> rollnumber;

if ((c = rollnumber % 10) == 0)

{

c = 3;

}

rollnumber = rollnumber / 10;

if ((b = rollnumber % 10) == 0)

{

if (c == 3)

{

b = 3;

c = 5;

}

else

{

b = 3;

}

rollnumber = rollnumber / 10;

if ((a = rollnumber % 10) == 0)

{

if (b == 3)

{

a = 3;

b = 5;

}

else if (c == 3)

{

a = 3;

c = 5;

}

else

{

a = 3;

}

cout << "a = " << a << " b = " << b << " c = " << c;

// If column of first matrix in not equal to row of second matrix,

// ask the user to enter the size of matrix again.

// Storing elements of first matrix.

cout << endl

<< "Enter elements of matrix 1:" << endl;

for (i = 0; i < a; i++)

{

for (j = 0; j < b; j++)

{

cout << "Enter element X - " << i + 1 << j + 1 << " : ";

cin >> X[i][j];

}

// Storing elements of second matrix.

cout << endl

<< "Enter elements of matrix 2:" << endl;

for (i = 0; i < b; i++)

for (j = 0; j < c; j++)

{

cout << "Enter element Y - " << i + 1 << j + 1 << " : ";

cin >> Y[i][j];

}

// Initializing elements of matrix Z to 0.

for (i = 0; i < a; i++)

for (j = 0; j < c; j++)

{

Z[i][j] = 0;

}

// multiplying matrix a and b and storing in array Z.

for (i = 0; i < a; i++)

{

for (j = 0; j < c; j++)

{

for (k = 0; k < b; k++)

{

Z[i][j] += X[i][k] * Y[k][j];

}

cout << endl

<< "X Matrix: " << endl;

for (i = 0; i < a; i++)

{

for (j = 0; j < b; j++)

{

cout << " " << X[i][j];

}

cout << endl;

}

cout << endl

<< "Y Matrix: " << endl;

for (i = 0; i < b; i++)

{

for (j = 0; j < c; j++)

{

cout << " " << Y[i][j];

}

cout << endl;

}

// Displaying the multiplication of two matrix.

cout << endl

<< "Output Matrix: " << endl;

for (i = 0; i < a; i++)

{

for (j = 0; j < c; j++)

{

cout << " " << Z[i][j];

}

cout << endl;

}

return 0;

}

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