# C Program to Find Scalar Multiplication of a Matrix

• Write a C program to multiply a scalar number and a matrix
• C program for scalar multiplication of a matrix.

There are two kinds of matrix multiplication, scalar multiplication and matrix multiplication. Matrix multiplication is multiplication of two matrices whereas scalar multiplication is multiplication of a matrix and a single number.

In matrix algebra, a real number is called a scalar. The scalar product of a real number s, and a matrix A is the matrix sA. In scalar multiplication of matrix, we simply multiply each element of the matrix by a scalar number.
Algorithm of scalar multiplication of matrix
Let s be scalar (real numbers) and A be a m x n matrix.
• To multiply a matrix with a number, we multiply each element of matrix with that number.
• Traverse every element of matrix using two loops.
• For every element A[i][j], multiply it with scalar s and stores the result back in A[i][j](A[i][j] = A[i][j] x s)

## C program to find scalar multiplication of a matrix.

```/*
* C Program to find scalar multiplication of a matrix
*/

#include <stdio.h>
#include <conio.h>

int main(){
int rows, cols, rowCounter, colCounter, scalar;
int inputMatrix;
printf("Enter Rows and Columns of Matrix\n");
scanf("%d %d", &rows, &cols);

printf("Enter Matrix of size %dX%d\n", rows, cols);
/*  Input matrix*/
for(rowCounter = 0; rowCounter < rows; rowCounter++){
for(colCounter = 0; colCounter < cols; colCounter++){
scanf("%d", &inputMatrix[rowCounter][colCounter]);
}
}
/*  Input scalar number*/
printf("Enter a number to multiply with matrix \n");
scanf("%d", &scalar);
/* Multiply each element of matrix with scalar*/
for(rowCounter = 0; rowCounter < rows; rowCounter++){
for(colCounter = 0; colCounter < cols; colCounter++){
inputMatrix[rowCounter][colCounter] = inputMatrix[rowCounter][colCounter]*scalar;
}
}

printf("Product Matrix\n");
for(rowCounter = 0; rowCounter < rows; rowCounter++){
for(colCounter = 0; colCounter < cols; colCounter++){
printf("%d ", inputMatrix[rowCounter][colCounter]);
}
printf("\n");
}
getch();
return 0;
}
```

Program Output
```Enter Rows and Columns of Matrix
2 2
Enter Matrix of size 2X2
0 1
2 1
Enter a number to multiply with matrix
2
Product Matrix
0 2
4 2
```
```Enter Rows and Columns of Matrix
2 3
Enter Matrix of size 2X2
1 2 0
2 8 1
Enter a number to multiply with matrix
-3
Product Matrix
-3 -6 0
-6 -24 -3
```

Properties of scalar multiplication of matrix
Let s and t be scalar (real numbers) and A and B are m x n matrix.
• Commutative : sA = As
• Associative : s(tA) = (st)A
• Distributive : (s + t)A = sA + tA and t(A + B) = tA + tB
• Identity : 1 · A = A
• If A id a mxn matrix then sA is also a mxn matrix

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