Numerical Methods: Multiplication of two matrices using two dimensional array in C
Let we have two 2 x 2 matrices A and B
\[ A = \begin{bmatrix} a_{00} & a_{01}\\
a_{10} & a_{11}
\end{bmatrix} \text{ and } B = \begin{bmatrix} b_{00} & b_{01} \\
b_{10} & b_{11} \end{bmatrix}\]
The multiplication of $A$ and $B$ works as follows
\[ A = \begin{bmatrix} a_{00} & a_{01}\\
a_{10} & a_{11}
\end{bmatrix} \text{ and } B = \begin{bmatrix} b_{00} & b_{01} \\
b_{10} & b_{11} \end{bmatrix}\]
The multiplication of $A$ and $B$ works as follows
- Multiply $a_{00}$ with $b_{00}$ and $a_{01}$ with $b_{10}$ and sum them together. So the first element $r_{00}$ becomes $a_{00}$ . $b_{00}$ + $a_{01}$ . $b_{10}$
- Multiply $a_{00}$ with $b_{01}$ and $a_{01}$ with $b_{11}$ and sum them together. So the first element $r_{01}$ becomes $a_{00}$ . $b_{01}$ + $a_{01}$ . $b_{11}$
- Multiply $a_{10}$ with $b_{00}$ and $a_{11}$ with $b_{10}$ and sum them together. So the first element $r_{10}$ becomes $a_{10}$ . $b_{00}$ + $a_{11}$ . $b_{10}$
- Multiply $a_{10}$ with $b_{01}$ and $a_{11}$ with $b_{11}$ and sum them together. So the first element $r_{11}$ becomes $a_{10}$ . $b_{01}$ + $a_{11}$ . $b_{11}$
So the resulting matrix $R$ becomes,
\[ R = \begin{bmatrix} a_{00}.b_{00}+a_{01}.b_{10} & a_{00}.b_{01} + a_{01}.b_{11} \\ a_{10}.b_{00} + a_{11}.b_{10} & a_{10}.b_{01} + a_{11}.b_{11}\end{bmatrix}\]
Note: In order to multiply two matrices, $A$ and $B$, the number of columns in $A$ must equal the number of rows in $B$. Thus, if $A$ is an $m * n$ matrix and $B$ is an $r * s$ matrix, $n = r$.
Note: In order to multiply two matrices, $A$ and $B$, the number of columns in $A$ must equal the number of rows in $B$. Thus, if $A$ is an $m * n$ matrix and $B$ is an $r * s$ matrix, $n = r$.
Source Code
#includeint main() { int r1, c1, r2, c2, matrix1[10][10], matrix2[10][10], result[10][10]; int i, j, k; printf("Enter the row and column of the first matrix: "); scanf("%d%d",&r1,&c1); printf("Enter the row and column of the second matrix: "); scanf("%d%d",&r2,&c2); if(c1 != r2){ printf("Matrix multiplication impossible"); } printf("Enter the first matrix: \n"); for(i = 0; i