Table of contents  
Matrices Addition  
Matrices Subtraction  
Matrices Multiplication  
Key Points 
The addition of two matrices A_{m * n} and B_{m * n }gives a matrix C_{m * n}. The elements of C are sum of corresponding elements in A and B which can be shown as:
The algorithm for addition of matrices can be written as:
for i in 1 to m
for j in 1 to n
c_{ij} = a_{ij }+ b_{ij}
// C++ Program for matrix addition
#include <iostream>
using namespace std;
int main()
{
int n = 2, m = 2;
int a[n][m] = { { 2, 5 }, { 1, 7 } };
int b[n][m] = { { 3, 7 }, { 2, 9 } };
int c[n][m];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
c[i][j] = a[i][j] + b[i][j];
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++)
cout << c[i][j] << " ";
cout << endl;
}
}
Output:
5 12
3 16
Time Complexity: O(n * m)
Auxiliary Space: O(n * m)
Key points:
The subtraction of two matrices A_{m * n} and B_{m * n} gives a matrix C_{m * n}. The elements of C are difference of corresponding elements in A and B which can be represented as:
The algorithm for subtraction of matrices can be written as:
for i in 1 to m
for j in 1 to n
c_{ij} = a_{ij}b_{ij}
// C++ Program for matrix substraction
#include <iostream>
using namespace std;
int main()
{
int n = 2, m = 2;
int a[n][m] = { { 2, 5 }, { 1, 7 } };
int b[n][m] = { { 3, 7 }, { 2, 9 } };
int c[n][m];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
c[i][j] = a[i][j]  b[i][j];
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++)
cout << c[i][j] << " ";
cout << endl;
}
}
Output:
1 2
1 2
Key points:
The multiplication of two matrices A_{m * n} and B_{n * p} gives a matrix C_{m * p}. It means number of columns in A must be equal to number of rows in B to calculate C = A * B. To calculate element c11, multiply elements of 1st row of A with 1st column of B and add them (5 * 1 + 6 * 4) which can be shown as:
The algorithm for multiplication of matrices A with order m*n and B with order n*p can be written as:
for i in 1 to m
for j in 1 to p
c_{ij} = 0
for k in 1 to n
c_{ij} + = a_{ik }* b_{kj}
// C++ Program for matrix Multiplication
#include <iostream>
using namespace std;
int main()
{
int n = 2, m = 2;
int a[n][m] = { { 2, 5 }, { 1, 7 } };
int b[n][m] = { { 3, 7 }, { 2, 9 } };
int c[n][m];
int i, j, k;
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
c[i][j] = 0;
for (k = 0; k < n; k++)
c[i][j] += a[i][k] * b[k][j];
}
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
cout << c[i][j] << " ";
cout << endl;
}
}
Output:
16 59
17 70
65 videos120 docs94 tests

1. What are the different operations that can be performed on matrices? 
2. How is matrix addition performed? 
3. What is the process of matrix subtraction? 
4. How is matrix multiplication carried out? 
5. What are the key points to remember while performing operations on matrices? 

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