**Write a program in c to multiply a scalar number(real number) and 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[50][50]; 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

**Related Topics**