Instruction
1
By definition, the matrix C, the product of matrices A and B consists of elements[i,j], each of which is equal to the sum of products of elements of row i of the matrix A by the corresponding elements of column j of matrix B. This can be written by formula. The formula takes into account that the matrix A has dimension m x p and matrix B is p x n. Then the matrix C will have the dimension m x n.
How to multiply the matrix
2
Let's consider an example. Multiply the matrices A and B indicated in the figure. Consistently we find all the elements of the matrix C = AB.
[1,1] = a[1,1]*b[1,1] + a[1,2]*b[2,1] + a[1,3]*b[3,1] = 3*2 + 2*5 + 0*3 = 16
c[1,2] = a[1,1]*b[1,2] + a[1,2]*b[2,2] + a[1,3]*b[3,2] = 3*1 + 2*4 + 0*2 = 11
c[2,1] = a[2,1]*b[1,1] + a[2,2]*b[2,1] + a[2,3]*b[3,1] = 1*2 + 3*5 + 1*3 = 20
c[2,2] = a[2,1]*b[1,2] + a[2,2]*b[2,2] + a[2,3]*b[3,2] = 1*1 + 3*4 + 1*2 = 15
How to multiply the matrix