Here is the 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.
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.
#include <stdio.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);
for(rowCounter = 0; rowCounter < rows; rowCounter++){
for(colCounter = 0; colCounter < cols; colCounter++){
scanf("%d", &inputMatrix[rowCounter][colCounter]);
}
}
printf("Enter a number to multiply with matrix \n");
scanf("%d", &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");
}
return 0;
}
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.
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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